Let P₂ represent real polynomials of degree 2 or less. Define a linear transformation T: P₂ → P₂ by T(p(x)) = −2p(x).If B represents the basis {1, x, x²} of P₂, write down the matrix [T] B. Let A and A' be a pair of similar 2 × 2 matrices. It is necessarily true that A - Id and A' - - Id are similar? If it is true, prove it. If it is not, show a counterexample.
Let P₂ represent real polynomials of degree 2 or less. Define a linear transformation T: P₂ → P₂ by T(p(x)) = −2p(x).If B represents the basis {1, x, x²} of P₂, write down the matrix [T] B. Let A and A' be a pair of similar 2 × 2 matrices. It is necessarily true that A - Id and A' - - Id are similar? If it is true, prove it. If it is not, show a counterexample.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![(b) Let P₂ represent real polynomials of degree 2 or less. Define a linear transformation T:
P2 → P₂ by T(p(x)) = −2p(x).If B represents the basis {1, x, x²} of P2, write down the
matrix [T]B.
(c) Let A and A' be a pair of similar 2 × 2 matrices. It is necessarily true that A – Id and
A' - Id are similar? If it is true, prove it. If it is not, show a counterexample.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd4ad3e1a-5eb7-4646-b724-5c75e9b9d297%2F63835712-6374-469f-9220-efbd09520a96%2Fwnr0ih_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(b) Let P₂ represent real polynomials of degree 2 or less. Define a linear transformation T:
P2 → P₂ by T(p(x)) = −2p(x).If B represents the basis {1, x, x²} of P2, write down the
matrix [T]B.
(c) Let A and A' be a pair of similar 2 × 2 matrices. It is necessarily true that A – Id and
A' - Id are similar? If it is true, prove it. If it is not, show a counterexample.
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