Short Questions and Answers

SHORT QUESTIONS AND ANSWERS

1. Find the power method, the largest Eigenvalue of  correct to two decimal places, choose [1, 1]^T as the initial Eigenvector.

Solution:

2. Determine the largest Eigenvalue and the corresponding Eigenvector of the matrix  correct to two decimal places using power method.

Solution :

3. The power method will work satisfactorily only if A has an ……….. Eigenvalue.

Solution :

Dominant

4. If the Eigenvalues of A are -3, 3, 1 then the dominant Eigenvalue of A is ………

Solution :

No dominant Eigenvalue

5. If the Eigenvalues of A are 1, 3, 4, then the dominant Eigenvalue of A is ……..

Solution : 4.

6. If the Eigenvalues of A are -4, 3, 1 then the dominant Eigenvalue of A is …..

Solution: -4

7. How will you find the smallest Eigenvalue of a square matrix A? (or) Write down the procedure to find the numerically smallest Eigenvalue of a matrix by power method. [A.U A/M 2010]

Solution:

By power method, the largest Eigenvalue of A^-1 can be found. Then, smallest Eigenvalue of A is the reciprocal of largest Eigenvalue of A^-1.

8. Explain power method to find the dominant Eigenvalue of a square matrix A. (or) Define power method.

Solution:

If Xo is an initial arbitrary vector, then compute

9. When do we use the power method? [A.U A/M 2015 (R8)]

Solution:

We use, the power method to find the largest Eigenvalue in magnitude and the corresponding Eigenvector of A.

10. When can we expect faster convergence in power method?

Solution :

We assume, | λ₁ | > | λ₂ | > … > | λ_n  

Faster convergence is obtained when | λ₂ | < | λ₁|

11. Does the power method give the sign of the largest Eigenvalue?

Solution :

No.

12. What is the use of power method ? [A.U M/J 2013]

Solution :

To find the numerically largest Eigenvalue of a given matrix.