Linear mapping/Kernel/2152 3-27-1 2-1-43/Exercise

Determine the kernel of the linear map

$\mathbb {R} ^{4}\longrightarrow \mathbb {R} ^{3},{\begin{pmatrix}x\\y\\z\\w\end{pmatrix}}\longmapsto {\begin{pmatrix}2&1&5&2\\3&-2&7&-1\\2&-1&-4&3\end{pmatrix}}{\begin{pmatrix}x\\y\\z\\w\end{pmatrix}}.$

To solution