Linear Algebra - Linear Algebra

56:  

Eigen values of

are

A.

0,0,0

B.

0,0,1

C.

0,0,3

D.

1,1,1

 
 

Option: C

Explanation :

Given matrix is 

Now

Hence eigen values are 0, 0, 3.

Click on Discuss to view users comments.

Write your comments here:



57:  

If R=

then top row of R-1 is

A.

[5  6  4]

B.

[5  -3  1]

C.

[2  0  1]

D.

[2  -1  1/2]

 
 

Option: B

Explanation :

Since, I R I = 1, therefore top row  [5  -3  1]

 

Click on Discuss to view users comments.

Write your comments here:



58:  

Sum of the eigen values of the matrix 

is

A.

5

B.

7

C.

9

D.

18

 
 

Option: B

Explanation :

Sum of eigen values of given matrix is

= summetion of element of diagonal of given matrix

=1 + 5 + 1

7

Click on Discuss to view users comments.

Write your comments here:



59:  

For which value of x, will the matrix 

become singular

A.

4

B.

6

C.

8

D.

12

 
 

Option: A

Explanation :

For singular matrix,

 8 [0 - 12] - x [0 - 2x12] = 0

 -96 + 24x = 0

 x = 4

Click on Discuss to view users comments.

Write your comments here:



60:  

Rank of the matrix, 

 

A.

1

B.

2

C.

3

D.

none of these

 
 

Option: B

Explanation :

Since, 

= 12 - 24 + 12 = 0

and Mn = 12 = 0.

Hence rank is 2.

Click on Discuss to view users comments.

Write your comments here: