Let P₂ be the vector space of polynomials of degree 2 or less. Consider the following two ordered bases of P₂: B = C = {2+ x − x², (−2) + x², 1+x}, {−1−x-x², −1− x², x²}. 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] = =

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.3: Vectors
Problem 11E
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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 =
C =
{2+x-x², (-2) + x², 1+x},
{-1-x-x², -1- x², x²}.
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: B = C = {2+x-x², (-2) + x², 1+x}, {-1-x-x², -1- x², x²}. 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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