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Chapter 7: Q40E (page 358)

Find all the eigenvalues and 鈥渆igenvectors鈥� of the linear transformations.

T(f)=f'-ffromC鈭�toC鈭�

Short Answer

Expert verified

The eigenvalues and eigenvectors of the linear transformations are,

位鈭�R,E位=spane位+35t

Step by step solution

01

Define eigenvalues

The scalar values that are associated with the vectors of the linear equations in the matrix are called eigenvalues.

Ax鈫�=位x鈫�,here x鈫�is eigenvector and位 is the eigenvalue.a

02

Determine all the eigenvalues and eigenvectors by substituting the given equation

Consider the given equation,

Tf=5f'-3f

Solve using the formula,

Tf=位蹿

Substitute the value for,T (f)

5f'-3f=位ff'=位+35ff(x)=C.e位+35x,C鈭�R

Thus, for an eigenvalue, the eigenvector space is e位+35t.

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Most popular questions from this chapter

Find all2脳2matrices for whiche鈬赌1is an eigenvector.

For a given eigenvalue, find a basis of the associated eigenspace. Use the geometric multiplicities of the eigenvalues to determine whether a matrix is diagonalizable. For each of the matrices A in Exercises 1 through 20, find all (real) eigenvalues. Then find a basis of each eigenspace, and diagonalize A, if you can. Do not use technology

14.(100-500001)

Find all 4x4matrices for whiche鈬赌2is an Eigen-vector.

if A is a 2脳2matrix with t r A = 5and det A = - 14what are the eigenvalues of A?

Find an eigenbasis for the given matrice and diagonalize:

A=[1111]
See all solutions

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