Let f : \mathbb{R}^{4} \to \mathbb{R}^{4} be the linear transformation defined by
f(w,x,y,z) = \left[\begin{array}{c}
-1\cr
0\cr
0\cr
0
\end{array}\right] w + \left[\begin{array}{c}
-3\cr
0\cr
0\cr
0
\end{array}\right] x + \left[\begin{array}{c}
-2\cr
2\cr
-1\cr
1
\end{array}\right] y + \left[\begin{array}{c}
5\cr
-4\cr
2\cr
-2
\end{array}\right] z.
Find bases for the kernel and image of f .
vector

A basis for the kernel off is \Big\lbrace \Big\rbrace.

A basis for the image off is \Big\lbrace \Big\rbrace.

A basis for the kernel of

A basis for the image of

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