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

Consider the linear map

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

such that

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

Compute

$\varphi {\begin{pmatrix}7\\6\end{pmatrix}}.$

Create a solution