True or False T F If A and B are both diagonal n x n matrice

True or False. T F: If A and B are both diagonal n x n matrices, then so is AB. T F: If A and B are both symmetric n x n matrices, then so is AB. T F: If A and B are n x n matrices such that A + B is symmetric, then A and B are also symmetric. T F: If A and B are n x n matrices such that A + B is upper triangular, then A and B are also upper triangular. T F: For any diagonal matrix A, the linear system Ax. = 0 has only the trivial solution x = 0. T F: For every linear transformation T: R^n rightarrow R^m, T(0) = 0. T F: If Ta : R3 rightarrow R^5 is the matrix transformation associated with a matrix A, then A is a 3 x 5 matrix. T F: If a matrix transformation Ta : R^n rightarrow K^m satisfies T^(x) = 0 for every x in R^n, then A is the m x n zero matrix. T F: There is at least one linear transformation T: R^n rightarrow R^m for which T(3x) = 5T(x) for some vector x in R^n. T F: If the matrix transformation T4: R^n rightarrow R^m associated with a matrix A satisfies Ta(x) = Ta(-x) for every vector x in R^n, then A is the m x n zero matrix.

Solution

(a) T
(b) F
(c) T
(d) F
(e) T
(f) T
(g) F
(h) F
(i) T
(j) T