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(d) Verify that for v= (a, b) E R², P[v]s' = [v]s and Q[v]s = [v]s•.

(d) Verify that for v= (a, b) E R², P[v]s' = [v]s and Q[v]s = [v]s•.

Advanced Engineering Mathematics
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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please just answer PART (D)

Let S = {(1,2), (2, 3)} and S' {(1,3), (1, 4)}, bases for R2. (a) For v = (a, b) in R², find [v]s and [v]s'. (b) Find P, the change of basis matrix from S to S'. (c) Find Q, the change of basis matrix from S' to S. (d) Verify that for v = (a, b) E R², P[v]s• = [v]s and Q[v]s = [v]s'.
Transcribed Image Text:Let S = {(1,2), (2, 3)} and S' {(1,3), (1, 4)}, bases for R2. (a) For v = (a, b) in R², find [v]s and [v]s'. (b) Find P, the change of basis matrix from S to S'. (c) Find Q, the change of basis matrix from S' to S. (d) Verify that for v = (a, b) E R², P[v]s• = [v]s and Q[v]s = [v]s'.
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