\subsection{Problem 13}

Let $\mathbf{Ax = b}$ , where $A = I_N \bigotimes C^TC$, the symbol $\bigotimes$ denotes the Kronecker product, $I_N \in R^{N \times N}$ is an identity matrix, $C \in R^{M \times M}$ is a random matrix with a uniform distribution, $M = 100$, and $N=50$, and $x \square N(0, I_{MN})$. Find the direct method that solves the above system  of  linear  equations  with  the  lowest  computational  cost.  Estimate  the  cost  with  a  roughly calculated number of flops and with the elapsed time.