Let T : R3 R3 be the linear operator defined by T(x1, x2, x3) = (x1 x2, x2 x1, x1 x3)

Chapter 8, Problem 6

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Let T : R3 R3 be the linear operator defined by T(x1, x2, x3) = (x1 x2, x2 x1, x1 x3) (a) Find the matrix for T with respect to the basis B = {v1, v2, v3}, where v1 = (1, 0, 1), v2 = (0, 1, 1), v3 = (1, 1, 0) (b) Verify that Formula (8) holds for every vector x = (x1, x2, x3) in R3. (c) Is T one-to-one? If so, find the matrix of T 1 with respect to the basis B.

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