SECTION 2.4 PROBLEM SET: INVERSE MATRICES In problems 1- 2, verify that the given matrices are inverses of each other. 3 -3 -1 0 3 -4 2 2) 2 -4 2 3 3 -5 In problems 3- 6, find the inverse of each matrix by the row-reduction method. 0 3) 4) 0 1 2 0SECTION 2.4 PROBLEM SET: INVERSE MATRICES Problems 9-10: Express the system as AX = B; then solve using matrix inverses found in problems 3-6. xty - Z= 2 10) x + y + z = 2 X Z = 7 3x + y = 7 23 + y + z = 13 x + y + 2z = 3 1 1) Why is if necessary that a matrix be > square 12) Suppose we are solving a system AX = B by matrix for its inverse to exist? Explain by the matrix inverse method, but discover A relating the matrix to a system of equations. has no inverse. How else can we solve this system? What can be said about the solutions of this system?SECTION 2.4 PROBLEM SET: INVERSE MATRICES In problems 5- 6, find the inverse of each matrix by the row-reduction method. Problems 7-1(f Express the system as AX = B; then solve using matrix inverses found in problems 3-6. 7 3Ix-5y =2 8 x + 2z _x+y' }"+4Z oo oo