Linear mapping/Determine image and kernel/Exercise

Determine the image and the kernel of the linear map

$f\colon \mathbb {R} ^{4}\longrightarrow \mathbb {R} ^{4},{\begin{pmatrix}x_{1}\\x_{2}\\x_{3}\\x_{4}\end{pmatrix}}\longmapsto {\begin{pmatrix}1&3&4&-1\\2&5&7&-1\\-1&2&3&-2\\-2&0&0&-2\end{pmatrix}}\cdot {\begin{pmatrix}x_{1}\\x_{2}\\x_{3}\\x_{4}\end{pmatrix}}.$

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