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.
Read the Matrices as Transformations lessons in full →
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”