5.) Let B = {(1,1, –1), (1,–1,1), (-1,1,1)}, and B' = {(1,0,0), (0,1,0), (0,0,1)} be bases for R³, and let 3 -1 A = 2 1 1 be the matrix for T: R3 → R³ relative to B. a.) Find the transition matrix P from B' to B. b.) Use the matrices P and A to find [v]g and [T(v)]B where [v]p' = [2 1 1]" c.) Find P-1 and A' (the matrix for T relative to B' d.) Find [T(v)]B, two ways. HIN112N5IN

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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In terms of Linear algebra. Please note all the parts for readability

5.) Let B = {(1,1, –1), (1,–1,1), (-1,1,1)}, and B' = {(1,0,0), (0,1,0), (0,0,1)} be bases for R3, and let
3
-1
2
1
11
2
A =
2
1
2
5
2
2-
be the matrix for T: R3 → R3 relative to B.
a.) Find the transition matrix P from B' to B.
b.) Use the matrices P and A to find [v]B and [T(v)]B where [v]p' = [2 1 1]"
c.) Find P-1 and A' (the matrix for T relative to B'
d.) Find [T(v)]B, two ways.
Transcribed Image Text:5.) Let B = {(1,1, –1), (1,–1,1), (-1,1,1)}, and B' = {(1,0,0), (0,1,0), (0,0,1)} be bases for R3, and let 3 -1 2 1 11 2 A = 2 1 2 5 2 2- be the matrix for T: R3 → R3 relative to B. a.) Find the transition matrix P from B' to B. b.) Use the matrices P and A to find [v]B and [T(v)]B where [v]p' = [2 1 1]" c.) Find P-1 and A' (the matrix for T relative to B' d.) Find [T(v)]B, two ways.
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