We consider the linear transformation T : R3 ------R 3 T(x,y,z) = ( x+2y-z, -x+y+2z, 3z) 1. Give the standard base B in R 3 2. Given the base B’ = (v1,v2,v3) V1 = [ 2 0 0 ] ; V2 = [ 1 4 0 ] ; V3 = [ −1 3 5 ] Find the matrix A’ of T in the base B’.

We consider the linear transformation T : R3 ------R 3 T(x,y,z) = ( x+2y-z, -x+y+2z, 3z) 1. Give the standard base B in R 3 2. Given the base B’ = (v1,v2,v3) V1 = [ 2 0 0 ] ; V2 = [ 1 4 0 ] ; V3 = [ −1 3 5 ] Find the matrix A’ of T in the base B’.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

We consider the linear transformation T : R3
------R
3
T(x,y,z) = ( x+2y-z, -x+y+2z, 3z)
1. Give the standard base B in R
3
2. Given the base B’ = (v1,v2,v3)
V1 = [
2
0
0
] ; V2 = [
1
4
0
] ; V3 = [
−1
3
5
]
Find the matrix A’ of T in the base B’.

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