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 $vec{v_1} = begin{bmatrix}1\1\1end{bmatrix}$
b) $vec{v_2} = begin{bmatrix}1\0\1end{bmatrix}$ is an eigenvector for A.
c) $vec{v_3} = begin{bmatrix}1\2\-1end{bmatrix}$ is in the image of A.