Linear mapping/Basis/(2,1,3) to (4,7) and (0,4,2) to (1,1) and (3,1,1) to (5,0)/(4,5,6)/Exercise

Consider the linear map

$\varphi \colon \mathbb {R} ^{3}\longrightarrow \mathbb {R} ^{2}$

such that

$\varphi {\begin{pmatrix}2\\1\\3\end{pmatrix}}={\begin{pmatrix}4\\7\end{pmatrix}},\,\varphi {\begin{pmatrix}0\\4\\2\end{pmatrix}}={\begin{pmatrix}1\\1\end{pmatrix}}{\text{ and }}\varphi {\begin{pmatrix}3\\1\\1\end{pmatrix}}={\begin{pmatrix}5\\0\end{pmatrix}}.$

Compute

$\varphi {\begin{pmatrix}4\\5\\6\end{pmatrix}}.$

Create a solution