Eigenvalue and Eigenvector Concepts

The video tutorial explains how to find an eigenvalue of a 3x3 matrix A using the eigenvector equation. It demonstrates solving for lambda by inspection and substitution, and verifies the result using a system of equations. The tutorial concludes with confirming that lambda equals -1/6.

What is the main task described in the introduction of the problem?

• To calculate the inverse of matrix A

• To solve a system of linear equations

• To find an eigenvalue of matrix A

• To find the determinant of matrix A

Which equation is used to relate matrix A and the given vectors?

• Inverse matrix equation

• Matrix multiplication equation

• Eigenvector equation

• Determinant equation

What does the vector equation indicate about the relationship between the vectors?

• They are parallel

• They are equal

• One is a scalar multiple of the other

• They are orthogonal

What is the purpose of substituting the vector into the equation?

• To verify the eigenvector

• To calculate the inverse

• To solve for lambda

• To find the determinant

How is lambda derived from the system of equations?

• By adding the equations

• By multiplying the equations

• By solving each equation separately

• By using the determinant

What is the first step in solving for lambda using the system of equations?

• Multiply all equations

• Divide each equation by its coefficient

• Subtract one equation from another

• Add all equations together

What is the value of lambda found in the solution?

• 1/6

• -1/6

• 1/3

• -1/3

Which equation is used to verify the value of lambda?

• The second equation

• The third equation

• The first equation

• All of the above

What is the significance of finding the same lambda from different equations?

• It shows the equations are dependent

• It confirms the solution is correct

• It suggests a need for further verification

• It indicates a mistake in calculations

What is the final conclusion of the problem?

• The eigenvalue is incorrect

• The vectors are not related

• An eigenvalue for matrix A is -1/6

• Matrix A is invertible