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
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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
%3D
12
8
[7(v)l8 =
8
(c) Find P-1 and A' (the matrix for T relative to B').
1/4
1/4
p-1=
9/8
-5/8
Transcribed Image Text: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 %3D 12 8 [7(v)l8 = 8 (c) Find P-1 and A' (the matrix for T relative to B'). 1/4 1/4 p-1= 9/8 -5/8
(c) Find P-1 and A' (the matrix for T relative to B').
-1/4
1/4
p-1=
9/8
-5/8
A' =
(d) Find [T(v)]B two ways.
[T(v)lg = P-[T(v)]B
%3D
[T(v)]B = A'[v]s
%3D
%3D
Transcribed Image Text:(c) Find P-1 and A' (the matrix for T relative to B'). -1/4 1/4 p-1= 9/8 -5/8 A' = (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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