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; Let P2 denote the vector space of all polynomials in the variable z of degree less than or equal to 2. Let C = {-1,3 – 3x, –3 – 3x + 1?} be an ordered basis for P2. a. Write (-4) + x² as a linear combination of elements from the basis C. (-4) + x² = (-1)+ (3 – 32)+ (-3 – 3x + x²). b. Let [glc denote the coordinate representation of q relative to the basis C. Find the coordinate vector representation for (-4) + x2 relative to the basis C. Your answer should be a vector of the general form <1,2,3>. [(-4) + 2²]c =

; Let P2 denote the vector space of all polynomials in the variable z of degree less than or equal to 2. Let C = {-1,3 – 3x, –3 – 3x + 1?} be an ordered basis for P2. a. Write (-4) + x² as a linear combination of elements from the basis C. (-4) + x² = (-1)+ (3 – 32)+ (-3 – 3x + x²). b. Let [glc denote the coordinate representation of q relative to the basis C. Find the coordinate vector representation for (-4) + x2 relative to the basis C. Your answer should be a vector of the general form <1,2,3>. [(-4) + 2²]c =

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.1: Orthogonality In Rn
Problem 10EQ: In Exercises 7-10, show that the given vectors form an orthogonal basis for2or3. Then use Theorem...
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: Let P2 denote the vector space of all polynomials in the variable a of degree less than or equal to 2. Let C = {–1,3 – 3r, –3 – 3x + 2²} be an ordered basis for P2. a. Write (-4) + x² as a linear combination of elements from the basis C. (-4) + z² = (-1)+ (3 — За)+ (-3 — Зг + г?). b. Let [glc denote the coordinate representation of q relative to the basis C. Find the coordinate vector representation for (-4) +x? relative to the basis C. Your answer should be a vector of the general form <1,2,3>. [(-4) + 2°]c =
Transcribed Image Text:: Let P2 denote the vector space of all polynomials in the variable a of degree less than or equal to 2. Let C = {–1,3 – 3r, –3 – 3x + 2²} be an ordered basis for P2. a. Write (-4) + x² as a linear combination of elements from the basis C. (-4) + z² = (-1)+ (3 — За)+ (-3 — Зг + г?). b. Let [glc denote the coordinate representation of q relative to the basis C. Find the coordinate vector representation for (-4) +x? relative to the basis C. Your answer should be a vector of the general form <1,2,3>. [(-4) + 2°]c =
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