1. You are given that the transition matrix PC,B from a basis B = {b1,b2,b3} to...

1. You are given that the transition matrix PC,B from a basis B = {b1,b2,b3} to a basis C = {c1,c2,c3} is

1 −1 0 2

1 0 1 −1 001

(a) For the vector u = b1 + b2 + 2b3, compute [u]C, and from this write down u as a linear combination of the vectors in C.
(b) Calculate PB,C.
(c) Suppose

c1 = (1,0,0), c2 = (1,2,0), c3 = (1,2,3).
Compute PS,B where S is the standard basis, and from this read off the explicit form

of the vectors b1, b2, b3.

Expert Solution

Colby Messinger answered 8 months ago

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