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-1 2 A = 2 1. pe the matrix for T: R3 - R3 relative to B. (a) Find the transition matrix P from B' to B. P= 2.

-1 2 A = 2 1. pe the matrix for T: R3 - R3 relative to B. (a) Find the transition matrix P from B' to B. P= 2.

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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5) PLEASE ANSWER EACH QUESTION, THANKS.

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