Solution Found!
In each of the following cases, find the eigenvalues and eigenvectors of the linear
Chapter 6, Problem 13(choose chapter or problem)
QUESTION:
In each of the following cases, find the eigenvalues and eigenvectors of the linear transformation T : P3 P3. a. T (p)(t) = p _ (t) b. T (p)(t) = tp _ (t) c. T (p)(t) = _ t 0 p _ (u) du d. T (p)(t) = t 2p __ (t) tp _ (t)
Questions & Answers
QUESTION:
In each of the following cases, find the eigenvalues and eigenvectors of the linear transformation T : P3 P3. a. T (p)(t) = p _ (t) b. T (p)(t) = tp _ (t) c. T (p)(t) = _ t 0 p _ (u) du d. T (p)(t) = t 2p __ (t) tp _ (t)
ANSWER:Step 1 of 8
a) Let
Note that standard basis of is.
Given.
Calculate :
Therefore the matrix is given as: