Question

Find the matrix representation A of the linear function: R²→R³ where

f(x,y)=(5x-y,2x-y,-x+2y) with respect to the standard bases for R² and R³

Answer 1

$f(x,y)=(5x-y,2x-y,-x+2y)\\ Canonical\ basis\ of\ \R^3\ is\\ \{(1,0,0),(0,1,0),(0,0,1)\}\\ \begin{bmatrix} 5 & -1 \\ 2 & -1\\ -1 & 2 \end{bmatrix}\begin{bmatrix} x \\ y \end{bmatrix}=\begin{bmatrix} 5x-y\\ 2x-y\\ -x+2y \end{bmatrix}$