-1 4 3] [5 2 Q1. [25 points] Consider the matrices A = 4 3 B...

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-1 4 3] [5 2 Q1. [25 points] Consider the matrices A = 4 3 B = 1 4 and 3 1 2. 12 4 -1 1 -5] C = -3 1 2 -2 1 a) [12 points] Determine whether any of A, B and C is symmetric, skew-symmetric (anti- symmetric), or none. Justify your answer in details. b) [6 points] Find another 3 × 3 matrix D, different from all of the above matrices, such that D is skew-symmetric (anti-symmetric). Justify your answer in details. c) [7 points] Use the above matrix B to verify that B + B" is a symmetric matrix. Do you think this is a rule that is always true for any matrix, or it is only true for this specific matrix? Justify your answer in details. -1 4 3] [5 2 Q1. [25 points] Consider the matrices A = 4 3 B = 1 4 and 3 1 2. 12 4 -1 1 -5] C = -3 1 2 -2 1 a) [12 points] Determine whether any of A, B and C is symmetric, skew-symmetric (anti- symmetric), or none. Justify your answer in details. b) [6 points] Find another 3 × 3 matrix D, different from all of the above matrices, such that D is skew-symmetric (anti-symmetric). Justify your answer in details. c) [7 points] Use the above matrix B to verify that B + B" is a symmetric matrix. Do you think this is a rule that is always true for any matrix, or it is only true for this specific matrix? Justify your answer in details.