Let B = {(1,1,0), (1,0, 1), (0, 1, 1)} and B' = {(1,0,0), (0,1,0), (0,0,1)} be bases for R°, and let 3 -1 2 A = 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]B and [T (v)]B, where [v]BI = [10 – 1]". (c) Find P-1 and A' (the matrix for T relative to B') (d) Find [T(v)]B/ in two ways. /2
Let B = {(1,1,0), (1,0, 1), (0, 1, 1)} and B' = {(1,0,0), (0,1,0), (0,0,1)} be bases for R°, and let 3 -1 2 A = 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]B and [T (v)]B, where [v]BI = [10 – 1]". (c) Find P-1 and A' (the matrix for T relative to B') (d) Find [T(v)]B/ in two ways. /2
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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![Let B = {(1,1,0), (1,0, 1), (0, 1, 1)} and B' = {(1,0, 0), (0, 1,0), (0,0, 1)} be bases for R³, and let
3
1
1
A =
1
1
be the matrix for T: R - R 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]B = [10 – 1]".
(c) Find P-1 and A' (the matrix for T relative to B')
(d) Find [T(v)]B in two ways.
2.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa75989a4-76ab-4f97-a89e-7dd957616e06%2F0735b67d-08ed-428f-8de6-29df84256ede%2Fpgbfw6o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let B = {(1,1,0), (1,0, 1), (0, 1, 1)} and B' = {(1,0, 0), (0, 1,0), (0,0, 1)} be bases for R³, and let
3
1
1
A =
1
1
be the matrix for T: R - R 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]B = [10 – 1]".
(c) Find P-1 and A' (the matrix for T relative to B')
(d) Find [T(v)]B in two ways.
2.
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