Linear projection/Basis/2 -5/4 3/Exercise

We consider the basis

${\begin{pmatrix}2\\-5\end{pmatrix}},{\begin{pmatrix}4\\3\end{pmatrix}}$

of ${}\mathbb {R} ^{2}$. Let ${}\varphi \colon \mathbb {R} ^{2}\rightarrow \mathbb {R} ^{2}$ denote the projection from ${}\mathbb {R} ^{2}$ to

${}\mathbb {R} {\begin{pmatrix}2\\-5\end{pmatrix}}\subseteq \mathbb {R} ^{2}\,$

with respect to this basis. Determine the matrix of ${}\varphi$ with respect to the standard basis.

Create a solution