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Let P2 be the vector space of polynomials of degree 2 or less. Consider the following two ordered bases of P2: B {x – x2, - x2, 1 – x + 2x?}, %3D C {1+x – x2, - 1+ a?, - 1- x + 2x2}. a. Find the change of basis matrix from the basis B to the basis C. [idg = b. Find the change of basis matrix from the basis C to the basis B. [id =

Let P2 be the vector space of polynomials of degree 2 or less. Consider the following two ordered bases of P2: B {x – x2, - x2, 1 – x + 2x?}, %3D C {1+x – x2, - 1+ a?, - 1- x + 2x2}. a. Find the change of basis matrix from the basis B to the basis C. [idg = b. Find the change of basis matrix from the basis C to the basis B. [id =

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 7EQ
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Let P2 be the vector space of polynomials of degree 2 or less. Consider the following two ordered bases of P2: {x – x2, – x², 1 – x + 2x²}, {1+ х — 2*, B – 1+ x², – 1 – x + 2x²}. a. Find the change of basis matrix from the basis B to the basis C. [id = b. Find the change of basis matrix from the basis C to the basis B. [id] =
Transcribed Image Text:Let P2 be the vector space of polynomials of degree 2 or less. Consider the following two ordered bases of P2: {x – x2, – x², 1 – x + 2x²}, {1+ х — 2*, B – 1+ x², – 1 – x + 2x²}. a. Find the change of basis matrix from the basis B to the basis C. [id = b. Find the change of basis matrix from the basis C to the basis B. [id] =
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