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