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Composing 3x3 matrices | Matrices | Precalculus | Khan Academy

Video vocabulary

nine

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US / naɪn /

UK / naɪn /

A1
  • number
  • 9

think

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US / θɪŋk /

UK / θɪŋk /

A1
  • verb
  • To have an idea about something without certainty
  • To have an idea, opinion or belief about something

partially

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US / ˈpɑ:ʃəli /

UK / ˈpɑ:rʃəli /

B1
  • adverb
  • In part; in some degree; not wholly

leave

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US / li:v /

UK / liv /

A1
  • noun
  • Permission to do something
  • Vacation time; time off work
  • verb
  • To go away from; depart
  • To gift property to someone after you die
  • To allow something to continue happening
  • To let something remain unused or available
  • To let something or someone remain somewhere

hopefully

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US / ˈhəʊpfəli /

UK / ˈhopfəli /

A2
  • adverb
  • In a manner wishing something to happen

over

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US / 'əʊvə(r) /

UK / ˈovɚ /

A1
  • adverb
  • Finished; no longer happening
  • Towards the ground/away from a standing position
  • noun
  • A set of six consecutive balls bowled in cricket
  • other
  • Finished
  • preposition
  • Showing the relation when a thing is above another
  • On or covering something
  • Above or across something
  • More than you need
  • From one side to the other
  • In the direction of; toward

composition

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US / ˌkɒmpəˈzɪʃn /

UK / ˌkɑ:mpəˈzɪʃn /

A2
  • noun
  • Piece of writing, music etc.
  • A piece of music
  • Structure of a picture or image to make an effect

another

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US / əˈnʌðə(r) /

UK / əˈnʌðɚ /

A1
  • adjecitve
  • One more, but not this
  • determiner
  • One more added
  • pronoun
  • One more (thing)

two

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US / tu: /

UK / tu /

A1
  • number
  • 2

and

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US / ənd /

UK / ənd, ən,ænd /

A1
  • conjunction
  • Used to refer to two or more things
  • Plus; in addition; on top of that
  • Used to introduce an action that follows another

vector

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US / 'vektə(r) /

UK / ˈvɛktɚ /

B2
  • noun
  • Math a quantity that has both size and direction

not

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US / nɒt /

UK / nɑt /

A1
  • adverb
  • Word indicating the negative
  • (Used to form the negative of verbs)

video

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US / 'vɪdɪəʊ /

UK / ˈvɪdiˌo /

A2
  • adjecitve
  • Of a moving film, with sound
  • noun
  • Recording capturing action with sound
  • verb
  • To make a moving film of, with sound

zero

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US / ˈzɪərəʊ /

UK / ˈzɪroʊ /

A1
  • noun
  • Temperature when water turns to ice
  • number
  • Number 0
  • verb
  • To set a scale or other device to show 0

yellow

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US / ˈjeləʊ /

UK / ˈjeloʊ /

A1
  • adjecitve
  • Color of lemons or the sun
  • Lacking in courage; cowardly (used as an INSULT)
  • verb
  • To turn yellow, often due to being old

represent

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US / ˌreprɪ'zent /

UK / ˌrɛprɪˈzɛnt /

A2
  • verb
  • To depict art objects, figures, scenes; to portray
  • To show or describe something in a particular way
  • To act on behalf of others in government
  • To act or speak for another person or other people

transform

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US / træns'fɔ:m /

UK / trænsˈfɔrm /

C2
  • verb
  • To change the shape completely in a good way

can

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US / kæn /

UK / kən,kæn /

A1
  • noun
  • A metal container for storing food
  • other
  • Able to; have the skill to; have the time to
  • verb
  • To have permission to
  • To be possible to do
  • To preserve food by sealing it in a metal container

would

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US / wʊd /

UK / wʊd /

A1
  • other
  • Used to indicate something imagined
  • Used to ask or request something politely
  • Verb used to indicate possibility, request etc.
  • Used to indicate a preference
  • Used to indicate a reaction
  • Indicates something that occurred repeatedly
  • Used to indicate willingness or ability to do

color

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US / 'kʌlə(r) /

UK / ˈkʌlɚ /

A1
  • noun
  • Quality of things you can see, e.g. red, blue
  • Pink or red in your face, e.g. after being ill
  • The shade of someone's skin e.g. black, or yellow
  • verb
  • To change or affect someone's opinion
  • To make something colorful using colored pencils

but

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US / bət /

UK / bʌt,bət /

A1
  • conjunction
  • Used before you say something different, opposite

apply

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US / ə'plaɪ /

UK / əˈplaɪ /

A1
  • verb
  • To spread a substance or liquid over a surface
  • To commit your time and effort to doing something
  • To make something useful in a certain situation
  • To be relevant for a situation
  • To ask formally for (job, permission etc.)

neat

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US / ni:t /

UK / nit /

A2
  • adjecitve
  • That you approve of; cool
  • (Of alcohol) not weakened with water or a mixer
  • Not messy; clean and orderly; simple and effective

now

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US / naʊ /

UK / naʊ /

A1
  • adverb
  • At the present time or moment
  • Right away or in the next possible moment
  • Used to refer to something that just happened
  • Time between the present and a moment in the past
  • conjunction
  • Resulting from or because of something

really

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US / ˈri:əli /

UK / ˈriəˌli, ˈrili /

A1
  • adverb
  • Used to stress something that is said; definitely
  • In a true or accurate manner
  • Very

those

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US / ðəʊz /

UK / ðoz /

A1
  • determiner
  • The people or things we are talking about
  • pronoun
  • The objects far from the speaker

reminder

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US / rɪˈmaɪndə(r) /

UK / rɪˈmaɪndər /

A2
  • noun
  • Something that causes one to remember something

just

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US / dʒʌst /

UK / dʒʌst /

A1
  • adjecitve
  • Proper or appropriate; as is deserved
  • Doing or being what is right or fair
  • Legally correct; having enough evidence
  • adverb
  • Almost; nearly
  • Exactly at the time of
  • Exactly (the same as, like)

column

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US / ˈkɒləm /

UK / ˈkɑ:ləm /

B1
  • noun
  • Regular series of articles in a newspaper/magazine
  • Strong vertical stone pillar that holds up a roof
  • Vertical line in a table or chart

through

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US / θru: /

UK / θru /

A2
  • adjecitve
  • having finished using or doing something
  • adverb
  • From the beginning of something until the end
  • preposition
  • Over, in, across an entire thing or place
  • Allowing you to pass between, or to
  • By a particular way or process; by the use of

middle

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US / 'mɪdl /

UK / ˈmidl /

A1
  • adjecitve
  • Equal distance from extremes
  • noun
  • Place that is halfway between two things

under

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US / ˈʌndə(r) /

UK / ˈʌndɚ /

A1
  • adjecitve
  • In the same place as another thing, but lower
  • adverb
  • In a lower quantity or price than expected
  • preposition
  • According to the terms of an agreement or law
  • Managed or controlled by the authority of
  • Being of a lesser quality or amount than expected
  • Influenced or affected by something or someone
  • Less or lower in age, amount, size or number

where

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US / hwɛə /

UK / hwɛr, wɛr /

A1
  • conjunction
  • At or in the place which
  • In whatever place
  • pronoun
  • Word you use to ask the location of something

complete

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US / kəm'pli:t /

UK / kəmˈplit /

A1
  • adjecitve
  • Being finished; done; achieved
  • Being as perfect and as total as could be
  • verb
  • To finish or reach the end of doing something

see

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US / si: /

UK / si /

A1
  • verb
  • To go on a date with someone
  • To predict whether something is, or will be true
  • To understand what someone says
  • To use your eyes to look at something
  • To visit a place often for sightseeing or pleasure
  • To visit or meet with someone
  • To find out by waiting or looking
  • To watch (a game, movie or TV show)

last

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US / lɑ:st /

UK / læst /

A1
  • adjecitve
  • Most recent; the latest
  • The one before
  • adverb
  • Final; with nothing following; after all others
  • Most recent; the latest
  • determiner
  • The one at the end
  • verb
  • To remain or continue for a certain period of time

could

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US / kəd /

UK / kʊd /

A1
  • other
  • Past form of 'can' to mean have ability
  • Used to ask for something politely, or to offer

six

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US / sɪks /

UK / sɪks /

A1
  • number
  • 6

with

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US / wɪð /

UK / wɪð, wɪθ /

A1
  • preposition
  • As an employee of a certain company
  • Against something or someone
  • By using something as a means
  • Due to; because of
  • Including
  • Possessing as a feature
  • Related to
  • (Of the manner/attitude by which you do something)
  • Used to express that people or things are together

away

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US / ə'weɪ /

UK / əˈwe /

A1
  • adjecitve
  • Not present
  • adverb
  • Disappear completely
  • Doing something with a lot of energy
  • Not here; far from here; in a different direction
  • To a different area, location

have

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US / həv /

UK / hæv /

A1
  • verb
  • To drink, smoke, eat or use something
  • To experience the effects of something
  • To organize an event, or join in an activity
  • To own, possess, or hold something
  • To cause to happen or produce a particular effect

blank

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US / blæŋk /

UK / blæŋk /

A2
  • verb
  • To make empty
  • To cause a memory to be erased
  • adjecitve
  • Showing no emotion or understanding
  • Being empty; not filled out; with no writing on it
  • noun
  • Empty space on a form which you fill in

unit

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US / ˈju:nɪt /

UK / ˈjunɪt /

B2
  • noun
  • One apartment in a building
  • Group of people, e.g. soldiers, that work together
  • A chapter of a textbook
  • A standard of measurement of something
  • Single item made by a company

negative

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US / 'neɡətɪv /

UK / ˈnɛɡətɪv /

A2
  • adjecitve
  • Being harmful, unwanted or unhelpful
  • In mathematics, being less than zero
  • Focusing on the bad aspects; pessimistic
  • noun
  • The opposite to a positive electrical charge
  • In grammar, containing words such as 'no' or 'not'
  • Reply to a question or statement that means 'no'
  • Image on camera film used to make a photo

situation

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US / ˌsɪtʃuˈeɪʃn /

UK / ˌsɪtʃuˈeʃən /

A1
  • noun
  • Place, position or area that something is in
  • Circumstance or condition surrounding an event
  • An unexpected problem or difficulty

time

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US / taɪm /

UK / taɪm /

A1
  • noun
  • Speed at which music is played; tempo
  • Point as shown on a clock, e.g. 3 p.m
  • Number of hours, minutes needed to do something
  • Occasion when something happens
  • Period or occasion that something occurred
  • Period in history or the past
  • Something measured in minutes, hours, days, etc.
  • How long an event takes; duration
  • verb
  • To check speed at which music is performed
  • To choose a specific moment to do something
  • To measure how long an event takes, e.g. a race
  • To schedule something to occur at a specific moment

pause

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US / pɔ:z /

UK / pɔz /

A2
  • noun
  • A temporary break before continuing
  • Function on a device to stop and restart it
  • Sign to hold a musical note a bit longer
  • verb
  • To stop doing for a while before continuing

question

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US / 'kwestʃən /

UK / ˈkwɛstʃən /

A1
  • noun
  • Issue or problems you are dealing with
  • What you ask about; issue
  • verb
  • To ask for or try to get information
  • To have or express concerns or uncertainty

math

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US / mæθ /

UK / mæθ /

A2
  • noun
  • Study or science of numbers and shapes

will

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US / wɪl /

UK / wɪl /

A1
  • noun
  • Desire or choice of someone
  • Document saying who gets your money when you die
  • Strong desire to do something; determination
  • Desire to do something; strong wish to do
  • other
  • Used with verbs to express the future
  • verb
  • To leave property to someone after your death
  • To use mental effort to make something happen
  • Am (is, are) likely to do
  • To influence someone to do something
  • To make something happen by strongly wanting it

after

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US / 'ɑ:ftə(r) /

UK / ˈæftɚ /

A1
  • adverb
  • Later than another time, or behind something
  • conjunction
  • Following something before
  • preposition
  • When an event happened or time has passed

write

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US / raɪt /

UK / raɪt /

A1
  • verb
  • To compose letters and words on paper or a screen
  • To invent or create a computer program
  • To create a song or piece of music

plus

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US / plʌs /

UK / plʌs /

A2
  • noun
  • A benefit or advantage
  • preposition
  • In addition; add
  • In addition to; Indicates a number above
  • Having a value greater than zero

try

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US / traɪ /

UK / traɪ /

A1
  • noun
  • Act of putting the ball over the rugby goal line
  • verb
  • To make an effort, to attempt to do something
  • To examine someone or something in a court of law
  • To test to see if it is good or you like it
  • To make a person go through hardship; test
  • To examine something to see if it works

use

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US / ju:s /

UK / ju:s /

A1
  • noun
  • Ability to employ something
  • Need to enable it to work
  • Permission to do something with something
  • Act of spending money
  • Operation of a machine for its function
  • verb
  • To have; to eat, drink, consume etc.
  • To need to operate or work
  • To operate a machine, e.g. a computer
  • To treat a person badly
  • To do something with, for a task or purpose

four

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US / fɔ:(r) /

UK / fɔr, for /

A1
  • number
  • 4

third

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US / θɜ:d /

UK / θɜ:rd /

A1
  • adjecitve
  • 3rd: Number after second

here

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US / hɪə(r) /

UK / hɪr /

A1
  • adverb
  • In this place; at this location, position or time

way

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US / weɪ /

UK / we /

A1
  • adverb
  • Used to emphasize the amount of something
  • noun
  • Particular aspect of something being thought about
  • One of various choices that could be made
  • Particular existing condition or state
  • (Often long) distance or length of time
  • How something is done
  • Route to go to a place
  • Small street
  • Usual behavior, emotions or habits of someone

add

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US / æd /

UK / æd /

A1
  • verb
  • To include as well
  • To put two things or numbers together, e.g. 2+2

all

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US / ɔ:l /

UK / ɔl /

A1
  • adverb
  • Completely; totally
  • determiner
  • Being every one of something
  • pronoun
  • 100% of something; the complete amount

transformation

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US / ˌtrænsfəˈmeɪʃn /

UK / ˌtrænsfərˈmeɪʃn /

C2
  • noun
  • A complete change in shape or form of something

direction

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US / də'rekʃn /

UK / dɪˈrɛkʃən, daɪ- /

A2
  • noun
  • When someone tells people what to do
  • Describes the way you are going, e.g. North

they

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US / ðeɪ /

UK / ðe /

A1
  • pronoun
  • Two or more people, animals, or things

work

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US / wɜ:k /

UK / wɚk /

A1
  • adjecitve
  • Activity completed in order to make money
  • noun
  • The product of some artistic or literary endeavor
  • Everything created by an author, artist, musician
  • Activity you do in order to make money
  • Place of employment
  • Final product or result of a some labor or effort
  • verb
  • To bring into a specific state of success
  • To be functioning properly, e.g. a car
  • To do your job in your company or workplace
  • To make an effort to do something
  • To operate a machine or device

bit

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US / bɪt /

UK / bɪt /

A1
  • noun
  • Device put in a horse's mouth to control it
  • Small piece of something
  • verb
  • (E.g. of fish) to take bait and be caught

take

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US / teɪk /

UK / tek /

A1
  • noun
  • Filming of a single scene for TV or the movies
  • verb
  • To accept something that is offered
  • To use a method of traveling, e.g. a bus or train
  • To use a camera to make (a photo)
  • To pick up something and go away with it
  • To study a subject in school
  • To attempt to pass (an exam)
  • To require a certain amount of time, money, space

space

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US / speɪs /

UK / spes /

A1
  • noun
  • Empty area kept for a specific reason, like a car
  • Empty area with nothing in it
  • Area in the sky where the stars are
  • Area between written words on a page
  • verb
  • To make a certain distance or time between

one

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US / wʌn /

UK / wʌn /

A1
  • pronoun
  • You; we; people in general; someone
  • The thing or person previously referred to
  • adjecitve
  • Used to refer to people generally
  • Being a strong example of (something mentioned)
  • number
  • Number 1

the

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US / ðə /

UK / ðə /

A1
  • article
  • Used to refer to something already mentioned
  • Used to show there is only one of something
  • determiner
  • Used to describe all of a family

image

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US / 'ɪmɪdʒ /

UK / ˈɪmɪdʒ /

A2
  • noun
  • Picture, sculpture or painting of something
  • General idea or opinion of something
  • verb
  • To obtain pictures by scanning them with a machine

quote

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US / kwəʊt /

UK / kwot /

A2
  • noun
  • Written statement of the cost of something
  • The (often wise or famous) words of another person
  • verb
  • To tell someone how much a task will cost
  • To repeat precisely what a person said or wrote

construct

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US / kənˈstrʌkt /

UK / kənˈstrʌkt /

A2
  • noun
  • A thought, theory or hypothesis
  • verb
  • To build or create something
  • To create a sentence, story, argument or theory

matrix

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US / ˈmeɪtrɪks /

UK / ˈmetrɪks /

B1
  • noun
  • Rock that surrounds rare stones
  • Pattern of lines, spaces, or numbers
  • Set of conditions that a person/thing develops in

how

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US / haʊ /

UK / haʊ /

A1
  • adjecitve
  • To what degree? in what amount?
  • adverb
  • (Used to explain the way to do something)
  • exclamation
  • For what purpose or reason?
  • (Used to ask someone or something's condition)

let

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US / let /

UK / lɛt /

A1
  • verb
  • To allow someone to do something
  • Introducing a suggestion to do something together
  • To rent a house, etc. to others

this

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US / ðɪs /

UK / ðɪs /

A1
  • adjecitve
  • Used to indicate something already been discussed
  • Used to indicate something happening around now
  • adverb
  • An indication by a physical motion or gesture
  • A specific amount of
  • determiner
  • Person, thing, or idea near you
  • pronoun
  • Person, thing that has already been discussed

three

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US / θri: /

UK / θri /

A1
  • number
  • Number 3

you

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US / jʊ /

UK / ju /

A1
  • pronoun
  • Person someone is speaking or writing to
  • Person or people in general

little

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US / 'lɪtl /

UK / ˈlɪtl /

A1
  • adjecitve
  • Being short in length of time
  • Not great in size, amount, or degree; small
  • Being very young or younger than others
  • adverb
  • By an amount or degree that is not very much
  • Not often; rarely
  • noun
  • A person's name

first

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US / fɜ:st /

UK / fɚst /

A1
  • adjecitve
  • 1st; Coming before all others in time or place
  • noun
  • Something that has not happened before
  • Position of the winner of a competition

thinking

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US / ˈθɪŋkɪŋ /

UK / ˈθɪŋkɪŋ /

A1
  • noun
  • Thoughts behind an idea, opinion or belief
  • verb
  • To have an idea, opinion or belief about something

each

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US / i:tʃ /

UK / itʃ /

A1
  • determiner
  • Every one of two or more things
  • pronoun
  • Per one person or thing

purple

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US / 'pɜ:pl /

UK / ˈpɚpəl /

A1
  • adjecitve
  • Being a color that is a mixture of red and blue

that

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US / ðæt /

UK / ðæt, ðət /

A1
  • adjecitve
  • The person or thing being talked about
  • Used to identify something both the speakers know
  • adverb
  • Used to reinforce adjectives and adverbs
  • To such a degree
  • conjunction
  • Used to connect a noun clause
  • Used to introduce an adverbial clause
  • Used to introduce a noun clause
  • determiner
  • Used as a noun to refer to something
  • pronoun
  • Referring an object far away
  • Used to refer to the relative pronoun ‘which’

right

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US / raɪt /

UK / raɪt /

A1
  • adjecitve
  • Correct or true
  • The south side of you looking at the rising sun
  • adverb
  • Exactly in a place or time
  • Being appropriate for a particular event
  • In a straight or direct manner
  • noun
  • Something you are legally or morally allowed to do
  • Ideal of what is just and good
  • Political view based on conservatism
  • verb
  • To fix something previously wrong or unjust
  • To make upright, as a boat that has turned over

then

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US / ðen /

UK / ðɛn /

A1
  • adverb
  • A time that is not now
  • Following another thing in time or arrangement
  • Following on reasonably from what was just stated
  • At that time, not now

about

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US / ə'baʊt /

UK / əˈbaʊt /

A1
  • adverb
  • To be ready to; going to
  • Nearly; approximately; roughly
  • Near; next to; close to
  • In every direction; in the area of
  • preposition
  • Concerning or of (a topic)

least

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US / li:st /

UK / list /

A1
  • adverb
  • In the smallest or lowest way
  • noun
  • Something that is of the lowest or smallest degree

get

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US / ɡet /

UK / ɡɛt /

A1
  • verb
  • To become affected by illness or disease
  • To begin to feel or understand an emotion or idea
  • To send or bring someone or something home, etc.
  • To go somewhere to obtain something
  • To (cause to) do a particular thing
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US / wɒt /

UK / hwɑt, hwʌt, wɔt, wʌt,hwət, wət /

A1
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  • Subtitles section
  • So we have two three-by-three matrices here, matrix A and matrix B. And we could, of course, view each of them as a transformation in three-dimensional space.
  • Now, what we're going to think about in this video is the composition of A of B. So you could think of this as the transformation where you apply B first and then you apply A after that.
  • And then we can represent that by another three-by-three matrix, which is partially completed here.
  • We have the first and the third column here.
  • And so my question to you is, what is this middle column where I have these three blanks?
  • Pause the video and try to work through that.
  • All right, now let's work through this together.
  • So one way to think about how to construct A of B is that what you're doing is you're taking each of the columns of B and you're thinking about what would they be under the transformation A. So if you were to apply the transformation A to this column right over here,
  • You would get this column.
  • If you apply the transformation A to this column right over here, you would get this column.
  • So what we really need to do is apply the transformation A to this column, to the middle column right over here.
  • And just as a reminder how this transformation works, a vector zero, two, three, you can think of it as zero of the one, zero, zero vector, the unit vector in the X direction, plus two of the zero, one,
  • Zero vector plus three of the zero, zero, one vector.
  • Now, when you apply the transformation, instead of using these unit vectors, you use the image of them under this transformation.
  • And now in this situation, instead of a one, zero, zero vector we are going to be using this thing.
  • Instead of a zero, one, zero, we're going to be using this thing.
  • Instead of a zero, zero, one, we are going to be using this thing.
  • So this middle column, when it's transformed by this vector is going to be zero, instead of the one, zero, zero, one, it's going to be zero of the negative three, negative three, three vector.
  • And then we have plus two, plus two of the zero, let me do that in a purple color, of the zero, negative two, three vector.
  • And then last but not least, you're going to have three of the, plus three of the, and I'll do that in yellow, the zero, negative four, one vector.
  • Now we just, quote, do the math.
  • So when you apply zero times all of this, you're just going to have a zero, zero, zero vector.
  • So we can, those all go away.
  • And then you are left with, let's see, this one is going to be two times zero is zero, two times negative two is negative four, two times three is six.
  • You're going to have that, plus three times zero is zero, three times negative four is negative 12, three times one is three.
  • I could have written this a little bit neater, but hopefully you get the idea.
  • And then when we add those two things, zero plus zero is zero.
  • Negative four plus negative 12 is negative 16.
  • Six plus three is nine.
  • And we're done.
  • We have just completed the composition of A of B.