9. Linear Transformations

Matrix Representations — Quiz

Test your understanding of matrix representations with 5 practice questions.

Practice Questions

Question 1

For the linear transformation $T:\mathbb{R}^2\to\mathbb{R}^2$ given by $T(x,y)=(3x-2y,\ x+4y)$, what is its matrix representation in the standard basis?

Question 2

If $T(e_1)=(1,0,2)$ and $T(e_2)=(-1,3,1)$, what is the standard matrix of $T:\mathbb{R}^2\to\mathbb{R}^3$?

Question 3

If $A=\begin{pmatrix}2 & 0\\5 & -1\end{pmatrix}$ represents $T$, what is $T\left(\begin{pmatrix}1\\3\end{pmatrix}\right)$?

Question 4

In the standard basis, the $j$-th column of a matrix representation of $T$ is the image of which vector?

Question 5

If $T$ has matrix $A$ and $S$ has matrix $B$, what matrix represents $S\circ T$?