In each of the following cases, find the eigenvalues and eigenvectors of the linear

Chapter 6, Problem 13

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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)

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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:

                 

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