Given the vectors $v_1 = (0, 1, 0, 2)$, $v_2 = (2, 0, -1, 0)$, $v_3 = (2, -1, 3, 2)$ and $u = (1, -1, 0, 1)$,\Use the Gram-Schmidt process to find an orthogonal basis for the subspace $W$ spanned by $v_1$, $v_2$ and $v_3$. \Find $Proj_wu$, the projection of $u$ onto the subspace $W$. Note: $Proj_wu = \alpha_1u_1 + \alpha_2u_2 + \alpha_3u_3$, where the $u_i$s are the orthogonal vectors generated in Part (a).\Calculate the error vector $u - Proj_wu$. \$A = (v_1|v_2|v_3)$, that is its columns are the vectors $v_1$, $v_2$, $v_3$. Find the solution $X$ of the system $A^TAx = A^Tu$. \Take $A\tilde{X}$ and compare it with what you got in Part (b). What do you get?