TF. In parts (a)(e) determine whether the statement is true or false, and justify your
Chapter 8, Problem TF(choose chapter or problem)
TF. In parts (a)(e) determine whether the statement is true or false, and justify your answer. (a) If the matrix of a linear transformation T : V W relative to some bases of V and W is 2 4 0 3 , then there is a nonzero vector x in V such that T(x) = 2x. (b) If the matrix of a linear transformation T : V W relative to bases for V and W is 2 4 0 3 , then there is a nonzero vector x in V such that T(x) = 4x. (c) If the matrix of a linear transformation T : V W relative to certain bases for V and W is 1 4 2 3 , then T is one-to-one. (d) If S: V V and T : V V are linear operators and B is a basis for V, then the matrix of S T relative to B is [T ]B[S]B. (e) If T : V V is an invertible linear operator and B is a basis for V, then the matrix for T 1 relative to B is [T ] 1 B
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