1. Consider the following vectors in R4: 2 1 H 0 The set B = {V₁, V2, V3} is a basis of some subspace V of Rª. V1 1 0 1 V2 V₂ = V3 2 -2 -1 3 a) Find an orthogonal basis D = {w₁, W2, w3} of the subspace V. 3 3 3 3

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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1. Consider the following vectors in Rª:
2
1
--0-0-0-0
-1
V3
=
1
-1
1
V2
2
-2
3
The set B = {V₁, V2, V3} is a basis of some subspace V of Rª.
=
a) Find an orthogonal basis D = {W₁, W2, W3} of the subspace V.
b) Compute the vector proju, the orthogonal projection of u onto V.
3
3
3
3
Transcribed Image Text:1. Consider the following vectors in Rª: 2 1 --0-0-0-0 -1 V3 = 1 -1 1 V2 2 -2 3 The set B = {V₁, V2, V3} is a basis of some subspace V of Rª. = a) Find an orthogonal basis D = {W₁, W2, W3} of the subspace V. b) Compute the vector proju, the orthogonal projection of u onto V. 3 3 3 3
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