Linear projection/Basis/3 7/4 -9/Exercise

We consider the basis

${\begin{pmatrix}3\\7\end{pmatrix}},{\begin{pmatrix}4\\-9\end{pmatrix}}$

in ${}\mathbb {R} ^{2}$. Let ${}\varphi \colon \mathbb {R} ^{2}\rightarrow \mathbb {R} ^{2}$ be the projection of ${}\mathbb {R} ^{2}$ onto ${}\mathbb {R} {\begin{pmatrix}3\\7\end{pmatrix}}\subseteq \mathbb {R} ^{2}$ with respect to this basis. Determine the matrix of ${}\varphi$ with respect to the standard basis.

Create a solution