Chapter 1 - Linear Equations in Linear Algebra - 1.8 Exercises - Page 69: 15

The linear transformation projects the vectors onto the vertical y axis.

$T(u)=\begin{bmatrix} 0&0\\ 0&1\\ \end{bmatrix}\begin{bmatrix} 5\\ 2\\ \end{bmatrix}=\begin{bmatrix} 0\\ 2\\ \end{bmatrix}$ $T(v)=\begin{bmatrix} 0&0\\ 0&1\\ \end{bmatrix}\begin{bmatrix} -2\\ 4\\ \end{bmatrix}=\begin{bmatrix} 0\\ 4\\ \end{bmatrix}$ The linear transformation projects the vectors onto the vertical y axis.