Let T1:M22 P1 and T2:P1 R3 be the linear transformations given by T1 a b c d = (a + b) +
Chapter 8, Problem 26(choose chapter or problem)
Let T1:M22 P1 and T2:P1 R3 be the linear transformations given by T1 a b c d = (a + b) + (c + d)x and T2(a + bx) = (a, b, a). (a) Find the formula for T2 T1. (b) Show that T2 T1 is not one-to-one by finding distinct 2 2 matrices A and B such that (T2 T1)(A) = (T2 T1)(B) (c) Show that T2 T1 is not onto by finding a vector (a, b, c) in R3 that is not in the range of T2 T1.
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