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

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.3: Change Of Basis
Problem 22EQ
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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:
{-1+x – x², 1– 2x + x², 1+ x},
{1+ г — 2?, — 1+ 2?, 2 — т?}.
B
C
-
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: {-1+x – x², 1– 2x + x², 1+ x}, {1+ г — 2?, — 1+ 2?, 2 — т?}. B C - 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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