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Problem #12 Part A) Prove that C = { 1 + x + x²₁ 1+ 2x, is a basis for 1R₂ [x] Part B) Consider another basis B = {1, x₁ x ² } for Ra[x]. Find the change of basis matrix from C to B. Part C) Find the coordinate vector of x with respect to C. That is, find [x]c -x+ 2x²3

Problem #12 Part A) Prove that C = { 1 + x + x²₁ 1+ 2x, is a basis for 1R₂ [x] Part B) Consider another basis B = {1, x₁ x ² } for Ra[x]. Find the change of basis matrix from C to B. Part C) Find the coordinate vector of x with respect to C. That is, find [x]c -x+ 2x²3

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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Problem #12 Part A) Prove that C = { 1 + x + x ²₁, 1+ 2x₁ = x+ 2x²} 2 is a basis for 1R₂ [x] Part B) Consider another basis B = { 1,₁ x₁, x² } for R₂[x]. Find the change of basis matrix from C to B. Part C) Find the coordinate vector of x with respect to C. That is, find [x]c
Transcribed Image Text:Problem #12 Part A) Prove that C = { 1 + x + x ²₁, 1+ 2x₁ = x+ 2x²} 2 is a basis for 1R₂ [x] Part B) Consider another basis B = { 1,₁ x₁, x² } for R₂[x]. Find the change of basis matrix from C to B. Part C) Find the coordinate vector of x with respect to C. That is, find [x]c
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