Would love some help with the steps in these, thank you

(Section 2.1) points 1. a. Given A = compute the following, iii. A2 - 2A + I b. If a polynomial p(x) can be factored as a product of two lower degree polynomials p1(x) and p2(x) as p(x) = P1(x)p2(z) then it can be proved that p( A) = p1(A)p2(A) for an arbitrary square matrix A. Verify this statement for polynomials p(x) = 22 -9, pi(x) = 1+3, p2(x) = x - 3. (Section 2.2) points Use the inversion algorithm to find the inverse of the matrix, if the inverse exists. 0 1 1 3 50 b. Find all values of c, if any, for which the given matrix is invertible. O 1 c1 10 1 c. Show that the matrices A and B are row equivalent by finding a sequence of elementary row operations that produces B from A, and then use that result to find a matrix C' such that CA = B. A = O B = -5 -1 0 -1 -2 -1(Section 2.3) 20 points 3. a. Solve the system by inverting the coefficient matrix and using Theorem 1.6.2 of the textbook. -x - 2y - 3z = 0 w + x+4y+42 =7 w + 3x+ 7y+9z =4 -w - 2x - 4y - 62 = 6 b. Determine conditions on the bj's, if any, in order to guarantee that the linear system is consistent. X1 - 212 - 23 = 61 -4x1 + 5x2 + 213 = b2 -4x1 + 712 + 413 = 63 (Section 2.4) 20 points 4. a. Find the diagonal entries of AB by inspection. 4 0 0 6 0 0 A = -2 0 0 B = 1 5 0 -3 0 7 3 2 6 b. Find a diagonal matrix A, given 9 0 0 A-2 = 10 4 0 10 0 (Section 2.5) 20 points 5. Consider an open economy with consumption matrix 1/2 1/4 1/4 C = 1/2 1/8 1/4 1/2 1/4 1/8 If the open sector demands the same dollar value from each product-producing sector, which such sector must produce the greatest dollar value to meet the demand? Is the economy productive