Question: 2. For the matrix A = (a) Determine AT. (b) Calculate A + AT and A - AT. (c) Prove that for all square matrices

2. For the matrix A = (a) Determine AT. (b) Calculate A + AT and A - AT. (c) Prove that for all square matrices A, A + A' is symmetric. (d) Find a symmetric matrix B (i.e. B' = B) and a skew-symmetric matrix C (i.e. CT = -C) for which A = B + C. (Hint: you can use part b).)

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