Matrices as Transformations flashcards

12 practice cards drawn from the Matrices as Transformations lessons. Tap a card to turn it over. Every answer is checked against the lesson it came from.

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Which matrix turns the plane a quarter turn counterclockwise?

(0 −1; 1 0)

from “Matrices as Transformations of the Plane”

Where does i land under this matrix?

(-2, 0)

from “Matrices as Transformations of the Plane”

The determinant of this matrix is 0. What happens to the unit square?

it is squashed onto a line

from “The Determinant as an Area Scale Factor”

By what factor does this matrix scale area?

2

from “The Determinant as an Area Scale Factor”

Q is done first, then P. Which product does both?

P Q

from “Composing Transformations by Multiplying Matrices”

Q acts first, then P. What goes in row 2, column 1 of the matrix that does both?

16

from “Composing Transformations by Multiplying Matrices”

How can a line be invariant when its points are not?

the points slide within the line

from “Invariant Points and Lines”

Which points does a rotation about the origin leave where they are?

the origin alone

from “Invariant Points and Lines”

Where does j land under this matrix?

(2, 1, 3)

from “Matrices as Transformations of Space”

Where does i land under this matrix?

(4, 3, 1)

from “Matrices as Transformations of Space”

The determinant of this matrix is 0. What happens to the unit cube?

it is flattened onto a plane

from “The Determinant as a Volume Scale Factor”

A solid of volume 3 is transformed by this matrix. What is its new volume?

72

from “The Determinant as a Volume Scale Factor”

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