Let P₁ be the set of polynomials of degree 1 or less. Consider the transformation t: P₁ → P₁ defined as follows: t(a + bx) = 4b 9ax a. Give the matrix for t relative to the standard basis of P b. Find the eigenvalues and the eigenvectors for the matrix. c. Give a basis B for P₁ such that RepBB t is diagonal, and give RepBB t in this basis.
Let P₁ be the set of polynomials of degree 1 or less. Consider the transformation t: P₁ → P₁ defined as follows: t(a + bx) = 4b 9ax a. Give the matrix for t relative to the standard basis of P b. Find the eigenvalues and the eigenvectors for the matrix. c. Give a basis B for P₁ such that RepBB t is diagonal, and give RepBB t in this basis.
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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Transcribed Image Text:Let P₁ be the set of polynomials of degree 1 or less. Consider the transformation t: P₁ → P₁ defined as follows:
t(a + bx) = 4b-9ax
a. Give the matrix for t relative to the standard basis of P
b. Find the eigenvalues and the eigenvectors for the matrix.
C. Give a basis B for P₁ such that RepÂ‚ß t is diagonal, and give RepBB t in this basis.
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