1 Let P = -3 -5 4 3 -1 0 5 1 U₁² = V1 ₁4₂ = ₁ 43 = - 3 2 V₂ -7 4, and V3 = 3 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 -9 4. Complete parts (a) and (b). 7

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.6: The Algebra Of Matrices
Problem 13E
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Question
Let P =
1
-3 -5
4
5
3 -1
0
1
=
V1
· 4₂ = ₁ 43 =
- 3
2
V2
-7
4, and V3 =
3
...
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
-9
4. Complete parts (a) and (b).
7
Transcribed Image Text:Let P = 1 -3 -5 4 5 3 -1 0 1 = V1 · 4₂ = ₁ 43 = - 3 2 V2 -7 4, and V3 = 3 ... 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 -9 4. Complete parts (a) and (b). 7
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 = ₁ W₂ = ₁ W₁ = [
□
Transcribed Image Text: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 = ₁ W₂ = ₁ W₁ = [ □
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