Let B = {(1, 3), (-2, –2)} and B' = {(-12, 0), (-4, 4)} be bases for R2, and let A- [:] 0 3 2 4 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 [T(v)]B, where [V]g = [2 -4]". [v]g -2 [T(v)]B = .......
Let B = {(1, 3), (-2, –2)} and B' = {(-12, 0), (-4, 4)} be bases for R2, and let A- [:] 0 3 2 4 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 [T(v)]B, where [V]g = [2 -4]". [v]g -2 [T(v)]B = .......
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
:]
0 3
A =
2 4
be the matrix for T: R → 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 [T(v)]p,
where
[v]g, = [2 -4]".
[v]g=
-2
[T(v)]B =
........](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4391da0a-9374-45f8-a9c6-851f56bfed48%2F0521e55f-694c-4e78-a91d-b960e85fc889%2F0wdnpfe_processed.png&w=3840&q=75)
Transcribed Image Text:Let B =
{(1, 3), (-2, -2)} and B' =
{(-12, 0), (-4, 4)} be bases for R2, and let
:]
0 3
A =
2 4
be the matrix for T: R → 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 [T(v)]p,
where
[v]g, = [2 -4]".
[v]g=
-2
[T(v)]B =
........
![1
(c) Find P- and A' (the matrix for T relative to B').
p-1 =
A' =
(d) Find [T(v)]g, two ways.
B'
[T(v)]g = P¯²[T(v)]g =
[T(v)]g = A'[v]g =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4391da0a-9374-45f8-a9c6-851f56bfed48%2F0521e55f-694c-4e78-a91d-b960e85fc889%2Flg8x23p_processed.png&w=3840&q=75)
Transcribed Image Text:1
(c) Find P- and A' (the matrix for T relative to B').
p-1 =
A' =
(d) Find [T(v)]g, two ways.
B'
[T(v)]g = P¯²[T(v)]g =
[T(v)]g = A'[v]g =
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