Use a software program or a graphing utility to (a) find the transition matrix from B to B′, (b) find the transition matrix from B′ to B, (c) verify that the two transition matrices are inverses of each other, and (d) find the coordinate matrix [x]B, given the coordinate matrix [x]B′.B = {(2, 0, −1), (0, −1, 3), (1, −3, −2)},B′ = {(0, −1, −3), (−1, 3, −2), (−3, −2, 0)},[x]B′ = [4 −3 −2]T
Use a software program or a graphing utility to
(a) find the transition matrix from B to B′,
(b) find the transition matrix from B′ to B,
(c) verify that the two transition matrices are inverses of each other, and
(d) find the coordinate matrix [x]B, given the coordinate matrix [x]B′.
B = {(2, 0, −1), (0, −1, 3), (1, −3, −2)},
B′ = {(0, −1, −3), (−1, 3, −2), (−3, −2, 0)},
[x]B′ = [4 −3 −2]T
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Basis: A set S is said to be a basis of a vector space V if S is linearly independent and the set S spans the
whole vector space V.
Part a
We have to find the transition matrix from the basis B to the basis B'.
Therefore, the transition matrix from B to B' is .
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