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Matrices Ex-3.3 Questions Answers

Subjects

Question 1 :

Find the transpose ofeach of the following matrices:

Answer 1 :

(i)  (ii)  (iii) 


Solution

(i) 

(ii) 

(iii) 

Question 2 :

If and, then verify that

Answer 2 :

(i) 

(ii) 


Solution

We have:

(i)

(ii)

Question 3 :

If and, then verify that

Answer 3 :

(i) 

(ii) 

Solution

(i) It is known that

Therefore, we have:

(ii)

Question 4 :

If and, then find 

Answer 4 :

We know that

Question 5 :

For the matrices A and B,verify that (AB)′ =  where

Answer 5 :

(i) 

(ii) 

Solution

(i)

(ii)

Question 6 :

If (i) , then verify that 

Answer 6 :

(ii) , then verify that 

Solution

(i)

(ii)

Question 7 :

(i) Show that thematrix is a symmetric matrix

Answer 7 :

(ii) Show that thematrix is a skew symmetric matrix

Solution


(i) We have:

Hence, A isa symmetric matrix.

(ii) We have:

Hence, A isa skew-symmetric matrix.

Question 8 :

For the matrix, verify that

Answer 8 :

(i)  is a symmetric matrix

(ii)  is a skew symmetric matrix

Solution

(i) 

Hence,  is a symmetric matrix.

(ii) 

Hence, is a skew-symmetric matrix.

Question 9 :

Find and, when 

Answer 9 :

The given matrix is