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Let B = {(1, 3), (-2,-2)) and B' = {(-12, 0), (-4, 4)) be bases for R2, and let A = 02 be the matrix for T: R2 R2 relative to B. (a) Find the transition matrix P from B' to B. P= (b) Use the matrices P and A to find [v]g and [7(V)]B, where [v]= [-14]. [v]8 = [T(V)]8 = (c) Find P¹ and A' (the matrix for 7 relative to B'). p-1 = QED 1 A¹ = 1

Let B = {(1, 3), (-2,-2)) and B' = {(-12, 0), (-4, 4)) be bases for R2, and let A = 02 be the matrix for T: R2 R2 relative to B. (a) Find the transition matrix P from B' to B. P= (b) Use the matrices P and A to find [v]g and [7(V)]B, where [v]= [-14]. [v]8 = [T(V)]8 = (c) Find P¹ and A' (the matrix for 7 relative to B'). p-1 = QED 1 A¹ = 1

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 B = {(1, 3), (-2,-2)) and B' = {(-12, 0), (-4, 4)) be bases for R2, and let A = 02 be the matrix for T: R² R2 relative to B. (a) Find the transition matrix P from B' to B. P= (b) Use the matrices P and A to find [v]g and [7(V)]B, where [v] = [-14]. [v]8 = [T(v)]8 = (c) Find P¹ and A' (the matrix for 7 relative to B'). p-1 = A¹ = 1 1 ↓↑ (d) Find [T(v)] two ways.
Transcribed Image Text:Let B = {(1, 3), (-2,-2)) and B' = {(-12, 0), (-4, 4)) be bases for R2, and let A = 02 be the matrix for T: R² R2 relative to B. (a) Find the transition matrix P from B' to B. P= (b) Use the matrices P and A to find [v]g and [7(V)]B, where [v] = [-14]. [v]8 = [T(v)]8 = (c) Find P¹ and A' (the matrix for 7 relative to B'). p-1 = A¹ = 1 1 ↓↑ (d) Find [T(v)] two ways.
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