(d) Show that the polynomials P₁ = 3 + 2x + x², P₂ = 2x+3x², p3= −2+x=2x² form a basis of the vector space P₂ of polynomials of degree at most 2 and find the coordinates of 1 + 2x - x² in this basis. Show your working.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.5: Basis And Dimension
Problem 65E: Find a basis for the vector space of all 33 diagonal matrices. What is the dimension of this vector...
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(d) Show that the polynomials
P₁ = 3 + 2x + x², P₂ = 2x+3x², p3= −2+x-2x²
form a basis of the vector space P₂ of polynomials of degree at most 2
and find the coordinates of 1 + 2x - x² in this basis. Show your working.
Transcribed Image Text:(d) Show that the polynomials P₁ = 3 + 2x + x², P₂ = 2x+3x², p3= −2+x-2x² form a basis of the vector space P₂ of polynomials of degree at most 2 and find the coordinates of 1 + 2x - x² in this basis. Show your working.
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