TF. In parts (a)(f) determine whether the statement is true or false, and justify your
Chapter 8, Problem TF(choose chapter or problem)
TF. In parts (a)(f) determine whether the statement is true or false, and justify your answer. (a) The composition of two linear transformations is also a linear transformation. (b) If T1: V V and T2: V V are any two linear operators, then T1 T2 = T2 T1. (c) The inverse of a one-to-one linear transformation is a linear transformation. (d) If a linear transformation T has an inverse, then the kernel of T is the zero subspace. (e) If T : R2 R2 is the orthogonal projection onto the x-axis, then T 1: R2 R2 maps each point on the x-axis onto a line that is perpendicular to the x-axis. (f ) If T1: U V and T2: V W are linear transformations, and if T1 is not one-to-one, then neither is T2 T1.
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