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Let 8 = {(1, 3), (-2,-2)} and 8' = {(-12, 0), (-4, 4)) be bases for R², and let A = - [83] be the matrix for 7: R² R² relative to 8. (a) Find the transition matrix P from 8' to 8. 6 4 P= 9 4 (b) Use the matrices P and A to find [v] and [7(v)]g, where [v]= [4 -1]. [v]g= Q [7(v)]a = (c) Find A-1 and A' (the matrix for 7 relative to 8'), p-1= - A'= (d) Find [7(v)]g two ways. [7(v)]g = P¹[7(v)]g = [7(v)]g¹ = A'[v]g' =

Let 8 = {(1, 3), (-2,-2)} and 8' = {(-12, 0), (-4, 4)) be bases for R², and let A = - [83] be the matrix for 7: R² R² relative to 8. (a) Find the transition matrix P from 8' to 8. 6 4 P= 9 4 (b) Use the matrices P and A to find [v] and [7(v)]g, where [v]= [4 -1]. [v]g= Q [7(v)]a = (c) Find A-1 and A' (the matrix for 7 relative to 8'), p-1= - A'= (d) Find [7(v)]g two ways. [7(v)]g = P¹[7(v)]g = [7(v)]g¹ = A'[v]g' =

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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Let 8 = {(1, 3), (-2,-2)} and 8' = {(-12, 0), (-4, 4)) be bases for R², and let A = - [83] be the matrix for 7: R² R² relative to 8. (a) Find the transition matrix P from 8' to 8. 6 4 P= 9 4 (b) Use the matrices P and A to find [v] and [7(v)]g, where [v]= [4 -1]. [v]g= Q [7(v)]a = (c) Find A-1 and A' (the matrix for 7 relative to 8'), p-1= - A'= (d) Find [7(v)]g two ways. [7(v)]g = P¹[7(v)]g = [7(v)]g¹ = A'[v]g' =
Transcribed Image Text:Let 8 = {(1, 3), (-2,-2)} and 8' = {(-12, 0), (-4, 4)) be bases for R², and let A = - [83] be the matrix for 7: R² R² relative to 8. (a) Find the transition matrix P from 8' to 8. 6 4 P= 9 4 (b) Use the matrices P and A to find [v] and [7(v)]g, where [v]= [4 -1]. [v]g= Q [7(v)]a = (c) Find A-1 and A' (the matrix for 7 relative to 8'), p-1= - A'= (d) Find [7(v)]g two ways. [7(v)]g = P¹[7(v)]g = [7(v)]g¹ = A'[v]g' =
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