Write x as the sum of two vectors, one in Span ({u₁,42,43) and one in Span (U4). Assume that {₁,...,4} is an orthogonal basis for R¹. 0 3 1 5 15 1 5 0 -3 -9 U₂ = u3 = U4 = X= 3 -4 0

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.4: The Singular Value Decomposition
Problem 33EQ
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Write x as the sum of two vectors, one in Span (u₁,U2,43} and one in Span {u4}. Assume that {u,₁,...,4} is an orthogonal basis for Rª.
3
1
5
15
1
5
- 3
- 9
U₁
U₂
000
u3
U4
X =
- 4
1
- 1
3
-1
1
- 4
1
0
X =
(Type an integer or simplified fraction for each matrix element.)
Transcribed Image Text:Write x as the sum of two vectors, one in Span (u₁,U2,43} and one in Span {u4}. Assume that {u,₁,...,4} is an orthogonal basis for Rª. 3 1 5 15 1 5 - 3 - 9 U₁ U₂ 000 u3 U4 X = - 4 1 - 1 3 -1 1 - 4 1 0 X = (Type an integer or simplified fraction for each matrix element.)
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