1 3 -1 - 7 Let P = -3 -5 v = 2 V2 and v3 = 3 . Complete parts (a) and (b). 4 1 5 a. Find a basis fu,, u2, u3} for R such that P is the change-of-coordinates matrix from {u1, U2, Uz} to the basis (v1. V2. V3}- [Hint: What do the columns of P C+ B represent?] - 12 – 11 -5 u, = -4 u, = - 9 Uz = 1 17 24 2 b. Find a basis {w,, w2, W3} for R such that P is the change-of-coordinates matrix from {v1. V2. V3} to (w1. W2. W3}. W2 W3
1 3 -1 - 7 Let P = -3 -5 v = 2 V2 and v3 = 3 . Complete parts (a) and (b). 4 1 5 a. Find a basis fu,, u2, u3} for R such that P is the change-of-coordinates matrix from {u1, U2, Uz} to the basis (v1. V2. V3}- [Hint: What do the columns of P C+ B represent?] - 12 – 11 -5 u, = -4 u, = - 9 Uz = 1 17 24 2 b. Find a basis {w,, w2, W3} for R such that P is the change-of-coordinates matrix from {v1. V2. V3} to (w1. W2. W3}. W2 W3
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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Please help with the second part. Thank you
![1
3 - 1
- 2
-6
Let P =
- 3 -5
v =
V2 =
and v3
3 . Complete parts (a) and (b).
4
5
1
2
a. Find a basis {u,, uz, uz) for R such that P is the change-of-coordinates matrix from {u1, uz, uz) to the basis {v1, v2, v3}. [Hint: What do the columns of P
C+B
represent?]
国国,回
- 12
- 11
-5
- 4
u, =
- 9
uz =
17
24
2
b. Find a basis {w,, w2, W3} for R such that P is the change-of-coordinates matrix from (V1, V2, V3) to (w1, W2, W3}).
w, =
w2 =
W3 =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcc357075-d330-4116-93bc-b2819b26405c%2F63805d40-1999-40c9-8953-81d1990247f6%2F70f92hw_processed.png&w=3840&q=75)
Transcribed Image Text:1
3 - 1
- 2
-6
Let P =
- 3 -5
v =
V2 =
and v3
3 . Complete parts (a) and (b).
4
5
1
2
a. Find a basis {u,, uz, uz) for R such that P is the change-of-coordinates matrix from {u1, uz, uz) to the basis {v1, v2, v3}. [Hint: What do the columns of P
C+B
represent?]
国国,回
- 12
- 11
-5
- 4
u, =
- 9
uz =
17
24
2
b. Find a basis {w,, w2, W3} for R such that P is the change-of-coordinates matrix from (V1, V2, V3) to (w1, W2, W3}).
w, =
w2 =
W3 =
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