Linear Algebra : Eigenvalues and Eigenvectors

Study concepts, example questions & explanations for Linear Algebra

varsity tutors app store varsity tutors android store

Example Questions

Example Question #11 : Eigenvalues And Eigenvectors

Possible Answers:

Correct answer:

Explanation:

Example Question #12 : Eigenvalues And Eigenvectors

Possible Answers:

Correct answer:

Explanation:

Example Question #13 : Eigenvalues And Eigenvectors

Possible Answers:

Correct answer:

Explanation:

Example Question #14 : Eigenvalues And Eigenvectors

Possible Answers:

Correct answer:

Explanation:

Example Question #15 : Eigenvalues And Eigenvectors

Possible Answers:

Correct answer:

Explanation:

Example Question #16 : Eigenvalues And Eigenvectors

Possible Answers:

Correct answer:

Explanation:

Example Question #17 : Eigenvalues And Eigenvectors

Possible Answers:

Correct answer:

Explanation:

Example Question #18 : Eigenvalues And Eigenvectors

Possible Answers:

Correct answer:

Explanation:

Example Question #19 : Eigenvalues And Eigenvectors

Possible Answers:

Correct answer:

Explanation:

Example Question #11 : Eigenvalues And Eigenvectors

Give the characteristic polynomial of the matrix

Possible Answers:

Correct answer:

Explanation:

The characteristic polynomial of a square matrix can be derived as follows:

Determine , using the identity matrix  with the same dimensions as  (two by two):

Subtract the matrices by subtracting elementwise:

Find the determinant of this matrix by taking the product of the upper left-to lower right diagonal and subtracting the product of the upper right-to-lower left diagonal:

,

the correct choice.

Learning Tools by Varsity Tutors