Find a single 3 3 matrix A for which all of the following properties are

true:

a) The kernel of A is the line spanned by the vector $\vec{v_1} = \begin{bmatrix}1\\1\\1\end{bmatrix}$

b) $\vec{v_2} = \begin{bmatrix}1\\0\\1\end{bmatrix}$ is an eigenvector for A.

c) $\vec{v_3} = \begin{bmatrix}1\\2\\-1\end{bmatrix}$ is in the image of A.