# Linear Algebra - Linear Algebra

26:

Given Matrix A=

The eigen-values are

 A. (3,4,2) B. (3,4,1) C. (3,4,5) D. (2,3,5) Answer Report Discuss Option: B Explanation : Click on Discuss to view users comments. Write your comments here:
27:

Given: matrix A=

The eigen vector corresponding to the smallest eigen value is

 A. B. C. D. None of these Answer Report Discuss Option: A Explanation : For finding eigen vector corresponding to 1,  putting λ equal to 1. Rank of the coefficient matrix= = Number of non-zero diagonal elements = 2 < 3. Hence non-zero solution vector = 3 - 2 = 1 These equation can berewritten as From these equations,    Hence is the required eigen vector. Click on Discuss to view users comments. Write your comments here:
28:

Rank the following (n+1)×(n+1)matrix, where a is areal number, is

 A. 1 B. 2 C. n D. dependent upon the value of A Answer Report Discuss Option: A Explanation : Click on Discuss to view users comments. Write your comments here:
 A. if a = b or   θ = n , where n is an integer B. always C. never D. if a cosθ ≠ b sinθ Answer Report Discuss Option: A Explanation : Click on Discuss to view users comments. Write your comments here:
30:

Eigen values of the system represented by

X =

 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1

X are
 A. 0, 0, 0, 0 B. 1, 1, 1, 1 C. 0, 0, 0, -1 D. 1, 0, 0, 0 Answer Report Discuss Option: D Explanation : Click on Discuss to view users comments. Write your comments here: