QUESTION 2 Given matrix A below, -2 3 0 -20 0 3 4 a- (6 pts.) What are the eigenvalues of A? b- (6 pts.) What are the eigenspaces corresponding to each eigenvalue? c- (6 pts.) What are the basis vectors of each eigenspace?QUESTION 3 Given a diagonalizing matrix P and a matrix A' such that A = PA'PI 1/ P = 5- 21VE 07 A' = 2 2/ 5 1/ 5 0 1] a- (3 pts.) What are the eigenvalues of A? b- (3 pts.) Are the eigenvectors of A orthogonal? c- (5 pts.) What is the expression of A" in terms of P and A' ? d- (5 points) Compute A" in rational form using the answer to part c.QUESTION 4 Given matrices A, B, C below, A = 1- (5 pts.)- Determine whether matrix A is diagonalizable. Show why or why not. 2- (5 pts.)- Determine whether matrix B is diagonalizable. Show why or why not. 3-(5 pts.)- Determine whether matrix B is orthogonally diagonalizable. Show why or why not. 4- (7 pts.)- Is matrix C orthogonally diagonalizable? If yes, use MATLAB to show matrices Q and D such that C = QDQ (show elements of Q and D as decimal numbers).QUESTION 5 Which of the following statements about symmetric matrices and diagonalization are true and why? a- All square matrices are diagonalizable. b- If nullity of a square matrix is not zero, one of its eigenvalues is zero. c- If a matrix is invertible, none of its eigenvalues is zero. d- All symmetric matrices are square, diagonalizable and have real eigenvalues e- A square matrix of order n is diagonalizable if it has n distinct eigenvalues. f- If A is symmetric, its eigenvectors corresponding to distinct eigenvalues are orthogonal g- If A is symmetric, for each eigenvalue of multiplicity k, the dimension of its corresponding eigenspace may be less than k.QUESTION 6 Given the system of first-order linear differential equations: y1' = dy 1/dt = 6 y1 + 12 y2 y2' = dy2/dt = 12 y1 + 6 y2 a- Write the system as a matrix equation and show the coefficieny matrix b- Find the e-values and e-vectors of the coefficient matrix c- Solve the system and write the expressions of y, (t) and y2(t) if y1 (0) = 0 and y2(0) = 1