Problem 4 [10 points]: Answer the following and explain how you got your answers:
1. What is the operator 2-norm of the matrix diag(7, 3, 2, 1, 0, 0, 0) ? R<sup>7×7</sup>?
2. Determine the vector $v_1$ for the SVD of the matrix:
$M = \begin{pmatrix} -3 & 3 \ -2 & 2 \ 0 & 0 \ 2 & -2 \ 3 & -3 \end{pmatrix}$
3. Using the value $v_1$ from the previous part. Determine the variance of $Mv_1$ and use this
to determine $\sigma_1$.
4. What is the second singular value $\sigma_2$ for the matrix $M$ above?