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Which of the following sets of polynomials form a basis for P₂? (i) P₁ = 1 + 4x + 6x², P2 3+x = (ii) p₁ 1 + x₂ P₂ = 4x + x², P3 = 1 + 5x + x² = 1.² P1 1, P2 = 1-6x, p3 = x, P4 = A) (i) and (iii) only (B) (i) only (C) (i) and (ii) only (D) none of them (E) (ii) and (iii) only (F) all of them G) (iii) only (H) (ii) only

Which of the following sets of polynomials form a basis for P₂? (i) P₁ = 1 + 4x + 6x², P2 3+x = (ii) p₁ 1 + x₂ P₂ = 4x + x², P3 = 1 + 5x + x² = 1.² P1 1, P2 = 1-6x, p3 = x, P4 = A) (i) and (iii) only (B) (i) only (C) (i) and (ii) only (D) none of them (E) (ii) and (iii) only (F) all of them G) (iii) only (H) (ii) only

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.3: Orthonormal Bases:gram-schmidt Process
Problem 17E: Complete Example 2 by verifying that {1,x,x2,x3} is an orthonormal basis for P3 with the inner...
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Which of the following sets of polynomials form a basis for P₂? (i) p₁ = 1 + 4x + 6x², P2 = 3 + x (ii) P1 = 1+x, P2 4x + x², P3 = 1 + 5x + x² (iii) P1 1, P2 1 - 6x, P3 = x, P4 = x² (A) (i) and (iii) only (B) (i) only (C) (i) and (ii) only (D) none of them (E) (ii) and (iii) only (F) all of them (G) (iii) only (H) (ii) only
Transcribed Image Text:Which of the following sets of polynomials form a basis for P₂? (i) p₁ = 1 + 4x + 6x², P2 = 3 + x (ii) P1 = 1+x, P2 4x + x², P3 = 1 + 5x + x² (iii) P1 1, P2 1 - 6x, P3 = x, P4 = x² (A) (i) and (iii) only (B) (i) only (C) (i) and (ii) only (D) none of them (E) (ii) and (iii) only (F) all of them (G) (iii) only (H) (ii) only
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