The transpose of a matrix A, aT , is obtained by
Chapter 5, Problem 15(choose chapter or problem)
The transpose of a matrix A, aT , is obtained by interchanging its rows and columns. Thus, if we denote the element in row i, column j of A by a(i, j), then aT (i, j) = a(j, i). a. Find aT for a = c 1 3 4 6 2 1 d b. Prove that if A is a square matrix, then A is symmetric if and only if aT = a. c. Prove that (aT ) T = a. d. Prove that (a + b) T = aT + bT . e. Prove that (a # b) T = bT # aT .
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