Let B1 = {u1, u2} and B2 = {v1, v2} be the bases for R2 in which u1 = (1, 2), u2 = (2
Chapter 4, Problem 7(choose chapter or problem)
Let B1 = {u1, u2} and B2 = {v1, v2} be the bases for R2 in which u1 = (1, 2), u2 = (2, 3), v1 = (1, 3), and v2 = (1, 4). (a) Use Formula (14) to find the transition matrix PB2B1 . (b) Use Formula (14) to find the transition matrix PB1B2 . (c) Confirm that PB2B1 and PB1B2 are inverses of one another. (d) Letw = (0, 1). Find [w]B1 and then use the matrixPB1B2 to compute [w]B2 from [w]B1 . (e) Letw = (2, 5). Find [w]B2 and then use the matrixPB2B1 to compute [w]B1 from [w]B2 .
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