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Let V = R³, the vector space over R of dimension 3. Give an example of a subspac dimerem bases of V. (c) Show that the following is a scalar product (,) on V: 3 a1 b₁ (u, v) := Sabi where u= a₂ v= b₂ i=1 a3 b3 example of a vector i di lungon of (e) Use the Gram-Schmidt Process (or otherwise) to find an orthogonal basis for V containing the vector w₁ = A 0 "

Let V = R³, the vector space over R of dimension 3. Give an example of a subspac dimerem bases of V. (c) Show that the following is a scalar product (,) on V: 3 a1 b₁ (u, v) := Sabi where u= a₂ v= b₂ i=1 a3 b3 example of a vector i di lungon of (e) Use the Gram-Schmidt Process (or otherwise) to find an orthogonal basis for V containing the vector w₁ = A 0 "

Advanced Engineering Mathematics
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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1. Let V = R³, the vector space over R of dimension 3. of IZ Give an example of a subspac WAL 1 diferent bases of V. (c) Show that the following is a scalar product (,) on V: 4 3 a (u, v) Σaibi where u = a2 v= b₂ i=1 b3 n example of a vector i with Tongun (e) Use the Gram-Schmidt Process (or otherwise) to find an orthogonal basis for V containing the vector w₁ = 0 = b₁
Transcribed Image Text:1. Let V = R³, the vector space over R of dimension 3. of IZ Give an example of a subspac WAL 1 diferent bases of V. (c) Show that the following is a scalar product (,) on V: 4 3 a (u, v) Σaibi where u = a2 v= b₂ i=1 b3 n example of a vector i with Tongun (e) Use the Gram-Schmidt Process (or otherwise) to find an orthogonal basis for V containing the vector w₁ = 0 = b₁
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