Claremont * VERY Due Date: October 12, 2011 Total: 100 points (each question is worth 10 points) 1. a. Prove that the inverse transpose operation [(A) (A)) respects matrix multiplication: (AB)=(A)(B). b. Verify this identity for A Claremont Graduate University School of Politics & Economics Mathematics for Economists I Problem Set 4 [[|] 2. A square matrix is called normal if it commutes with its transpose: A'AAA'. Find all normal 2 x 2 matrices. 3. Find the LDI! factorization of the matrices -00-0- M, 121 M= + [84] 012 b. 12 1 4. Prove that the 3 x 3 matrix A= 2 4 -1 cannot be factored as 1-13 A=LDI! 5. Determine the rank of the following matrices d. M = 0 4 -1-5 2 00 1210 0121 0012 e. 000 3 1 12-31-2 24-21-2