Question

In this problem, answer "True" or "False" for each question. Note: there is no partial credit for this problem. You must answer all parts correctly to receive credit. You will not be shown the correct answers for individual parts. 1. Let A be a square matrix. If the system Ax b has a unique solution, then A is invertible. O True False 2. If A is a square matrix then AT -A True False 3. Given four invertible square matrices A, B, C, and D of the same size, we have (ABCD)1 (CD) (AB)1 O True False 4. Given two square matrices A and B of the same size, we have (A + B(A B) A True False

Answer 1

Let A be a square matrix If the system Ax = 6 has a unique solution, then A is invertible True Ax = 6 x = A^-1 b mean A is invertible If A is square matrix then A^T = A false Let A = [1 3 2 4] A^T = [1 2 3 4] A notequalto A^T Given four invertible matrix A, B, C, D of some size we have (A B C D)^-1 = (CD)^-1 (AB)^-1 or (A B C D)^-1 = D^-1 C^-1 B^-1 A^-1 (CD)^-1 (AB)^-1 \r\n given two square matrix A & B of same size we have (A + B) (A - B) = A^2 - B^2 False (A + B) (A - B) A^2 - AB + BA - B^2 (now its not necessary that AB = BA, so false