Let B = {(1, 2), (-1, -1)} and B' = {(-4, 1), (0, 2)} be bases for R2, and let!3!A =be the matrix for T: R2 R2 relative to B.(a) Find the transition matrix P from B' to B.9.2(b) Use the matrices P and A to find [v]a and [T(v)lB, where[v]g = [2 -3]7.4[v]B%3D128[7(v)l8 =8(c) Find P-1 and A' (the matrix for T relative to B').1/41/4p-1=9/8-5/8 (c) Find P-1 and A' (the matrix for T relative to B').-1/41/4p-1=9/8-5/8A' =(d) Find [T(v)]B two ways.[T(v)lg = P-[T(v)]B%3D[T(v)]B = A'[v]s%3D%3D

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Let B = {(1, 2), (-1, -1)} and B' = {(-4, 1), (0, 2)} be bases for R2, and let %3D A = be the matrix for T: R2 R2 relative to B. (a) Find the transition matrix P from B' to B. P = 9 (b) Use the matrices P and A to find [v]a and [T(v)lB, where [v]g = [2 -3] 4 [v]B: %3D 12 [7(v)lB 8 (c) Find P-1 and A' (the matrix for T relative to B'). 1/4 1/4 p-1= 9/8 -5/8

Let B = {(1, 2), (-1, -1)} and B' = {(-4, 1), (0, 2)} be bases for R2, and let %3D A = be the matrix for T: R2 R2 relative to B. (a) Find the transition matrix P from B' to B. P = 9 (b) Use the matrices P and A to find [v]a and [T(v)lB, where [v]g = [2 -3] 4 [v]B: %3D 12 [7(v)lB 8 (c) Find P-1 and A' (the matrix for T relative to B'). 1/4 1/4 p-1= 9/8 -5/8

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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