Classical

Linear Algebra - Linear Algebra

11:  

 If AT = A-1, where A is a real matrix, then A is

A. normal
B. symmetric
C. Hermitian
D. orthogonal
 
 

Option: D

Explanation :


12:  

 If A and B are non-zero square matrices, then AB = 0 implies

A. A and B are orthogonal
B. A and B are singular
C. B is singular
D. A is singular
 
 

Option: A

Explanation :


13:  

 If A and B be real symmetric matrices of sizen n x n, then

A.

AAT = 1

B.

A = A-1

C.

AB = BA

D.

(AB)T = BA

 
 

Option: D

Explanation :


14:  

If, A, B, C are square matrices of the same order, then (ABC)-1 is equal to

A.

C-1A-1B-1

B.

C-1 B-1 A-1

C.

A-1 B-1C-1

D.

A-1 C-1 B-1

 
 

Option: B

Explanation :


15:  

 Consider the following statements
S1: Sum of the two singular n x n matrices may be non-singular
S2 : Sum of two the non-singular nx n matrices may be singular.
Which of the following statements is correct?

A.

S1 and S2 are both true

B.

S1 is true, S2 is false

C.

S1 is false, S2 is true

D.

S1 and S2 are both false

 
 

Option: A

Explanation :




Suggest an improvement