1. Consider the following vectors in R¹: 1 -H The set B = {V1, V2, V3} is a basis of some subspace V of R¹. V₂ = 2 -2 |--D V3 = U= 3 3 2 a) Find an orthogonal basis D = {w₁, W2, W3} of the subspace V. b) Compute the vector proi..u the orthogonal projection of u onto V 3 3 3
1. Consider the following vectors in R¹: 1 -H The set B = {V1, V2, V3} is a basis of some subspace V of R¹. V₂ = 2 -2 |--D V3 = U= 3 3 2 a) Find an orthogonal basis D = {w₁, W2, W3} of the subspace V. b) Compute the vector proi..u the orthogonal projection of u onto V 3 3 3
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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Transcribed Image Text:1. Consider the following vectors in R¹:
V₁ =
1
2
0
V3 =
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 projvu, the orthogonal projection of u onto V.
3
3
3
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