Eigenvalues and Eigenvectors Concepts

The video tutorial explains how to find the eigenvalues and eigenvectors of a 3x3 matrix. It begins with an introduction to the concepts and then demonstrates the process of calculating eigenvalues using the determinant method. The tutorial further explores finding eigenvectors for each eigenvalue, specifically for Lambda = -2, 4, and 6, using matrix operations and row reduction techniques.

What is the first step in finding the eigenvalues of a matrix?

• Finding the inverse of the matrix

• Calculating the determinant of (Lambda I - A)

• Performing row reduction

• Solving for the eigenvectors

Which method is used to evaluate the determinant in this tutorial?

• Laplace transform

• Expansion by minors

• Cramer's rule

• Gaussian elimination

What is the eigenvalue corresponding to Lambda sub 1?

• 4

• -2

• 6

• 0

How is the eigenvector for Lambda sub 1 parameterized?

• T, 0, 0

• 3T, 2T, 0

• T, T, T

• 0, 0, T

What is the eigenvalue corresponding to Lambda sub 2?

• -2

• 4

• 0

• 6

How is the eigenvector for Lambda sub 2 parameterized?

• T, T, T

• -5T, 10T, 2T

• 0, 0, T

• T, 0, 0

What is the eigenvalue corresponding to Lambda sub 3?

• 4

• -2

• 6

• 0

How is the eigenvector for Lambda sub 3 parameterized?

• T, T, T

• -1T, 2T, 0

• T, 0, 0

• 0, 0, T

What is the span of the eigenvectors corresponding to Lambda = 4?

• 3, 2, 0

• 0, 0, 0

• -1, 2, 0

• -5, 10, 2

What is the span of the eigenvectors corresponding to Lambda = 6?

• -1, 2, 0

• 0, 0, 0

• -5, 10, 2

• 3, 2, 0