5. Let $v_1 = \begin{bmatrix} 0 \ 1/\sqrt{2} \ 1/\sqrt{2} \end{bmatrix}$, $v_2 = \begin{bmatrix} 0 \ 1/\sqrt{2} \ -1/\sqrt{2} \end{bmatrix}$, $x = \begin{bmatrix} 2 \ 1 \ 1 \end{bmatrix}$, $v_3 = \begin{bmatrix} 1 \ 0 \ 0 \end{bmatrix}$, $u_i = proj_{v_i}x$, $c_i = \begin{bmatrix} c_1 \ c_2 \ c_3 \end{bmatrix}$ and $U = [v_1, v_2, v_3]$. Determine which of the following is false.
$v_i \cdot x = v_i^T x$, $i = 1, 2, 3$. Let $C = \begin{bmatrix} c_1 \ c_2 \ c_3 \end{bmatrix}$ and $U = [v_1, v_2, v_3]$. Determine which of the
following is false.
a. $x = UC$ b. $||C||^2 = ||x||^2$ c. $C = \begin{bmatrix} 1 \ 3/\sqrt{2} \ 1/\sqrt{2} \end{bmatrix}$ d. $C = U^Tx$ e. None of these
