Let T1: R2 R2 and T2: R2 R2 be the linear operators given by the formulas T1(x, y) = (x
Chapter 8, Problem 22(choose chapter or problem)
Let T1: R2 R2 and T2: R2 R2 be the linear operators given by the formulas T1(x, y) = (x + y, x y) and T2(x, y) = (2x + y, x 2y) (a) Show that T1 and T2 are one-to-one. (b) Find formulas for T 1 1 (x, y), T 1 2 (x, y), (T2 T1) 1 (x, y) (c) Verify that (T2 T1)1 = T 1 1 T 1 2 .
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