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

Let a linear mapping

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

satisfying

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

be given. Compute

$\varphi {\begin{pmatrix}3\\-5\\4\end{pmatrix}}.$

Create a solution