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Linear Algebra

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Moderate

Standard Matrix of a Shear

LINALG-XTYPXW

Which of the following matrices is the standard matrix of a linear transformation $T:\mathbb{R}^2\to\mathbb{R}^2$ that sends the unit square $[0,1]\times[0,1]$ to a non-rectangular parallelogram?

A

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

B

$\begin{pmatrix}1&0\\\ 7&1\end{pmatrix}$

C

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

D

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

E

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