Classical

Linear Algebra - Linear Algebra

16:  

 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 :

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kabil said: (5:11pm on Sunday 1st September 2013)
i thing option b may be correct because two singular matrix satisfy.but two non singular matrix doesn't satisfy. sorry if i did wrong
Haradhan said: (1:22am on Monday 29th January 2018)
I thing option A true.as for ex... A=(2 1) B=(-2 1) THEN A B=(0 2) is singular . (12) (-1 1) (0 3)

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17:  

Rank of the matrix

 
0 0 -3
9 3 5
3 1 1
 
A.

0

B.

1

C.

2

D.

-1

 
 

Option: C

Explanation :

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18:  

Rank of matrix 

 
1 4 8 7
0 0 3 0
4 3 2 1
3 12 24 2
 
A.

3

B.

1

C.

2

D.

4

 
 

Option: D

Explanation :

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19:  

Let A = ( ai) be an n-rowed square matrix and I12 be the matrix obtained by interchanging the first and second rows of the n-rowed identity matrix. Then AJ12 is such that its first

A.

row is the same as its second row

B.

row is the same as the second row of A

C.

column is the same as the second column of A

D.

row is all zero

 
 

Option: C

Explanation :

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20:  

Eigen vector(s) of the matrix

 
0 0 α
0 0 0
0 0 0
 

is(are)

A.

(0,0 ,α)

B.

(α,0,0)

C.

(0,0,1)

D.

(0,α,0)

 
 

Option: D

Explanation :

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