Let $$A=\left[\begin{array}{cc} 9 &-9\cr -3 &3 \end{array}\right].$$
Find bases for the kernel and image of $T(\vec{x}) = A \vec{x}$.

A basis for the kernel of $A$ is $\Bigg\lbrace$ $\left[\Rule{0pt}{2.4em}{0pt}\right.$$\left]\Rule{0pt}{2.4em}{0pt}\right.$ $\Bigg\rbrace.$

A basis for the image of $A$ is $\Bigg\lbrace$ $\left[\Rule{0pt}{2.4em}{0pt}\right.$$\left]\Rule{0pt}{2.4em}{0pt}\right.$ $\Bigg\rbrace.$