1 3 - 1 - 3 -9 - 8 Let P = - 3 -5 ,v1 = 4 V2 = 6. and v3 = 2 Complete parts (a) and (b). 4 1 4 7 a. Find a basis (u,, u2, u3} for R° such that P is the change-of-coordinates matrix from (u,, u2, u3} to the basis (v,, v2, V3}. [Hint: What do the columns of P represent?] C+ B 8 - 4 - 5 u, = u2 = -8 , u3 = - 2 18 21 b. Find a basis (w,, w2, W3} for R such that P is the change-of-coordinates matrix from {V1, V2, V3} to (w,, W2, W3}. W, = W2 = W3 =
1 3 - 1 - 3 -9 - 8 Let P = - 3 -5 ,v1 = 4 V2 = 6. and v3 = 2 Complete parts (a) and (b). 4 1 4 7 a. Find a basis (u,, u2, u3} for R° such that P is the change-of-coordinates matrix from (u,, u2, u3} to the basis (v,, v2, V3}. [Hint: What do the columns of P represent?] C+ B 8 - 4 - 5 u, = u2 = -8 , u3 = - 2 18 21 b. Find a basis (w,, w2, W3} for R such that P is the change-of-coordinates matrix from {V1, V2, V3} to (w,, W2, W3}. W, = 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
Related questions
Question
![1
3
- 1
- 3
- 9
- 8
Let P =
0 , v1 =
Complete parts (a) and (b).
-3 -5
V2 =
6.
and
V3
2
%3D
4
1
4
7
a. Find a basis fu,, u2, uz} for R° such that P is the change-of-coordinates matrix from fu,, U2, uz} to the basis (v,, v2, V3}. [Hint: What do
the columns of
P represent?]
С+ В
- 8
- 4
- 5
u1
- 6
U2 =
- 8
, U3
- 2
%3D
18
21
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}:
W1
W2
, W3
%3D
%D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3128d9e2-e802-40b2-a444-5ed816f99dd9%2F69d6943e-f53c-4499-920d-7145b76bb01d%2Fe1yoq8t_processed.png&w=3840&q=75)
Transcribed Image Text:1
3
- 1
- 3
- 9
- 8
Let P =
0 , v1 =
Complete parts (a) and (b).
-3 -5
V2 =
6.
and
V3
2
%3D
4
1
4
7
a. Find a basis fu,, u2, uz} for R° such that P is the change-of-coordinates matrix from fu,, U2, uz} to the basis (v,, v2, V3}. [Hint: What do
the columns of
P represent?]
С+ В
- 8
- 4
- 5
u1
- 6
U2 =
- 8
, U3
- 2
%3D
18
21
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}:
W1
W2
, W3
%3D
%D
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