Let $V$ be the plane with equation $x_1 - 2 x_2 + 4 x_3 =0$ in ${\mathbb R}^3$. Find the matrix $A$ of the orthogonal projection onto the line spanned by the vector $\vec{v}= \left[\begin{array}{c} 16\cr 4\cr -2 \end{array}\right]$ with respect to the basis $\left\lbrace \left[\begin{array}{c} 2\cr 1\cr 0 \end{array}\right], \left[\begin{array}{c} -4\cr 0\cr 1 \end{array}\right] \right\rbrace.$

$A=$ $\left[\Rule{0pt}{2.4em}{0pt}\right.$$\left]\Rule{0pt}{2.4em}{0pt}\right.$