Let B = {(1, 3), (-2,-2)} and B' = {(-12, 0), (-4,4)} be bases for R2, and let - [²9] 43 be the matrix for T: R2 → R² relative to B. A = (a) Find the transition matrix P from B' to B. P= p-1 = 6 9 A' = (c) Find P-¹ and A' (the matrix for T relative to B'). -1/3 3/4 13 -33/2 ↓ 1 4 4 1/3 -1/2 ↓1 20/3 -8 ↓ 1 → (d) Find [7(v)]g two ways. [T(v)]B¹ = P¹[T(v)]B = (b) Use the matrices P and A to find [v] and [7(V)]B, where [V]B = [2 -5]T. [T(v)]B¹ = A'[v]B' = X X [v] = [T(v)]B = 7 -19 ↓ 1 7 -19 ↓ 1 X -8 -2 7 -19 ↓1 - → J
Let B = {(1, 3), (-2,-2)} and B' = {(-12, 0), (-4,4)} be bases for R2, and let - [²9] 43 be the matrix for T: R2 → R² relative to B. A = (a) Find the transition matrix P from B' to B. P= p-1 = 6 9 A' = (c) Find P-¹ and A' (the matrix for T relative to B'). -1/3 3/4 13 -33/2 ↓ 1 4 4 1/3 -1/2 ↓1 20/3 -8 ↓ 1 → (d) Find [7(v)]g two ways. [T(v)]B¹ = P¹[T(v)]B = (b) Use the matrices P and A to find [v] and [7(V)]B, where [V]B = [2 -5]T. [T(v)]B¹ = A'[v]B' = X X [v] = [T(v)]B = 7 -19 ↓ 1 7 -19 ↓ 1 X -8 -2 7 -19 ↓1 - → J
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
- [²9]
43
be the matrix for T: R2 → R² relative to B.
A =
(a) Find the transition matrix P from B' to B.
P=
p-1 =
6
9
A' =
(c) Find P-¹ and A' (the matrix for T relative to B').
-1/3
3/4
13
-33/2
↓ 1
4
4
1/3
-1/2
↓1
20/3
-8
↓ 1
→
(d) Find [7(v)]g two ways.
[T(v)]B¹ = P¹[T(v)]B =
(b) Use the matrices P and A to find [v] and [7(V)]B, where
[V]B = [2 -5]T.
[T(v)]B¹ = A'[v]B' =
X
X
[v] =
[T(v)]B =
7
-19
↓ 1
7
-19
↓ 1
X
-8
-2
7
-19
↓1
-
→
J](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8b8a4ad9-b66e-4dbe-8b3f-39bf0adb3cae%2Fc946dbd1-bf61-471b-8d38-9e428d283aa4%2Fvzvapx_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
- [²9]
43
be the matrix for T: R2 → R² relative to B.
A =
(a) Find the transition matrix P from B' to B.
P=
p-1 =
6
9
A' =
(c) Find P-¹ and A' (the matrix for T relative to B').
-1/3
3/4
13
-33/2
↓ 1
4
4
1/3
-1/2
↓1
20/3
-8
↓ 1
→
(d) Find [7(v)]g two ways.
[T(v)]B¹ = P¹[T(v)]B =
(b) Use the matrices P and A to find [v] and [7(V)]B, where
[V]B = [2 -5]T.
[T(v)]B¹ = A'[v]B' =
X
X
[v] =
[T(v)]B =
7
-19
↓ 1
7
-19
↓ 1
X
-8
-2
7
-19
↓1
-
→
J
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