?

Linear Algebra

Free Version

Upgrade subject to access all content

Moderate

Finding STD Matrix from Values

LINALG-1U4NQ0

Suppose $T:\mathbb{R}^3\to\mathbb{R}^2$ is a linear transformation, and let:

$$v_1=\begin{pmatrix}1\\\ 0\\\ 1\end{pmatrix}$$
$$v_2=\begin{pmatrix}0\\\ 1\\\ 1\end{pmatrix}$$
$$v_3=\begin{pmatrix}0\\\ 0\\\ 1\end{pmatrix}$$

If:

$$T(v_1)=\begin{pmatrix}0\\\ 0\end{pmatrix}$$
$$T(v_2)=\begin{pmatrix}-1\\\ 1\end{pmatrix}$$
$$T(v_3)=\begin{pmatrix}2\\\ 2\end{pmatrix}$$

...then what is the standard matrix of $T$?

A

$\begin{pmatrix}-2&-3&2\\\ -2&-1&2\end{pmatrix}$

B

$\begin{pmatrix}2&-3&-2\\\ 2&-1&-2\end{pmatrix}$

C

$\begin{pmatrix}1&0&1\\\ 0&1&1\\\ 0&0&1\end{pmatrix}$

D

$\begin{pmatrix}0&-1&2\\\ 0&1&2\end{pmatrix}$

E

$\begin{pmatrix}1&0&0\\\ 0&1&0\\\ 1&1&1\end{pmatrix}$