Claremont * VERY Due Date: October 12, 2011 Total: 100 points (each question is worth 10...

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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 M₂= + [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. M₁ = 0 4 -1-5 2 00 1210 0121 0012 e. 000 3 1 12-31-2 24-21-2 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 M₂= + [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. M₁ = 0 4 -1-5 2 00 1210 0121 0012 e. 000 3 1 12-31-2 24-21-2

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Ill be happy to help you with your problem set Lets go through each question one by one 1a Prove that the inverse transpose operation AT1 A1T respects ... View the full answer