Now complete the following exercises which must be submitted and graded: 1. Consider the matrix $A=\left\begin{array}{ccccc} 1 & 2 & 5 & 2 & 13 & 0 & 2 & 0&3 10 & 2 & 3 & 2 & 0 1 1 & -1 & 2 & 1 & 1 1 1 & 2 & 3 & 4 & 5\end{array} ight]$ a. Find the inverse of matrix A. SHOW ALL ROW OPERATIONS USED!! b. Express $A^{-1}$ as a product of elementary matrices. c. Solve the linear system $A x=b$, where $b=\left[\begin{array}{c}17 15 13 11 W 9\end{array} ight]$, using $A^{-1}$. 2. Prove that if $A=\left\begin{array}{cca & b1c& d^{\prime} \end{array} ight]$, then $AC-1=\left\begin{array}{ccc} \frac{d}{a d-b c] & \frac{-b}{a d-b c] \frac{-cHa d-b c) & \frac{a} a d-b c) Vend{array} ight]$ SP.SD.3371