- 3 HG 4 4 5 1 2 Let P = - 3 1 3 - 1 W₁ = -5 0 - 4₂ = a. Find a basis (U₁, U₂, U3} for R³ such that P is the change-of-coordinates matrix from {U₁, U₂, U3} to the basis {V₁, V₂, V3}. [Hint: What do the columns of P represent?] C← B 4₁ = b. Find a basis {W₁, W₂, W3} for R³ such that P is the change-of-coordinates matrix from {V₁, V₂, V3} to {W₁, W₂, W3}. из = - 8 W₂ = ₁ W₂ 6 and V3 = = 4 -6 3 Complete parts (a) and (b 5
- 3 HG 4 4 5 1 2 Let P = - 3 1 3 - 1 W₁ = -5 0 - 4₂ = a. Find a basis (U₁, U₂, U3} for R³ such that P is the change-of-coordinates matrix from {U₁, U₂, U3} to the basis {V₁, V₂, V3}. [Hint: What do the columns of P represent?] C← B 4₁ = b. Find a basis {W₁, W₂, W3} for R³ such that P is the change-of-coordinates matrix from {V₁, V₂, V3} to {W₁, W₂, W3}. из = - 8 W₂ = ₁ W₂ 6 and V3 = = 4 -6 3 Complete parts (a) and (b 5
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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Question
CIRCLE THE ANSWERS!! AND CLEAR TO READ
![Let P =
1
- 3
4
U₁ =
3 - 1
0
1
- 5
01
W₂ =
5
■₁ U₂ = ₁ 43
=
3
W3
2
=
V₂
- 8
a. Find a basis (U₁, U2, U3} for R³ such that P is the change-of-coordinates matrix from
{U₁, U₂, U3} to the basis {V₁, V2, V3}. [Hint: What do the columns of
represent?]
4
and V3
- 6
3
5
Complete parts (a) and (b).
b. Find a basis {w₁, W₂, W3} for R³ such that P is the change-of-coordinates matrix from
{V₁, V₂, V3} to (W₁, W₂, W3}.
W₁ =
P
C← B](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8b6c3689-2b60-4c25-801e-fccc9acdd031%2F686e3e8b-21f6-4527-b01a-e1459caa6638%2Fovircx_processed.png&w=3840&q=75)
Transcribed Image Text:Let P =
1
- 3
4
U₁ =
3 - 1
0
1
- 5
01
W₂ =
5
■₁ U₂ = ₁ 43
=
3
W3
2
=
V₂
- 8
a. Find a basis (U₁, U2, U3} for R³ such that P is the change-of-coordinates matrix from
{U₁, U₂, U3} to the basis {V₁, V2, V3}. [Hint: What do the columns of
represent?]
4
and V3
- 6
3
5
Complete parts (a) and (b).
b. Find a basis {w₁, W₂, W3} for R³ such that P is the change-of-coordinates matrix from
{V₁, V₂, V3} to (W₁, W₂, W3}.
W₁ =
P
C← B
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