Question

Find the standard matrix of the linear transformation t(x, y, z) = (x − 2y + z, y − 2z, x + 3z).

Answer 1

$T(x,y,z)=(x-2y+z,y-2z,x+3z)=\begin{bmatrix}1&-2&1\\0&1&-2\\1&0&3\end{bmatrix}\begin{bmatrix}x\\y\\z\end{bmatrix}$