Chapter 5

Question 1

Find Eigenvalues ; matrix A & V

Answer 1

1. Multiply A and V.
2. Result is different than V. Find scalar that turns V into result.
3. Scalar is answer.

Question 2

Find Eigenvalues ; matrix A only

Answer 2

Main diagonal numbers are eigenvalues

Question 3

Calculate Characteristic Polynomial

Answer 3

1. Subtract lambda from main diagonal elements
2. ad - bc
3. Factor

Question 4

Find Eigenvector ( Basis Eigenspace )

Answer 4

1. Plug in eigenvalue. Subtract from main diagonal
2. Augment with 0 vector.
3. Row reduce all the way
4. Rightside of matrix is result eigenvector.

Question 5

Eigenvector is also known as

Answer 5

Basis of Eigenspace

Question 6

Basis of an Eigenspace is also a

Answer 6

Eigenvector

Question 7

How to Diagonalize matrix

Answer 7

1. Characteristic Polynomial
2. Eigenvalues are placed across main diagonal (D)
3. Apply Eigenvector process (P)