NCERT Solutions Class 12 Maths Chapter 3 - Matrices

 Page 1


Exercise 3.3 
Question 1:  
Find the transpose of each of the following matrices: 
(i) 
Answer 
 (i) 
(ii) 
(iii)  
( ii) ( iii) 
Page 2


Exercise 3.3 
Question 1:  
Find the transpose of each of the following matrices: 
(i) 
Answer 
 (i) 
(ii) 
(iii)  
( ii) ( iii) 
Question 2: 
If , then verify that 
(i) 
(ii)  
Answer We have: 
(i) 
(ii) 
and 
Page 3


Exercise 3.3 
Question 1:  
Find the transpose of each of the following matrices: 
(i) 
Answer 
 (i) 
(ii) 
(iii)  
( ii) ( iii) 
Question 2: 
If , then verify that 
(i) 
(ii)  
Answer We have: 
(i) 
(ii) 
and 
Question 3: 
If , then verify that  
(i) 
(ii) 
Answer 
(i) It is known that
Therefore, we have: 
and 
Page 4


Exercise 3.3 
Question 1:  
Find the transpose of each of the following matrices: 
(i) 
Answer 
 (i) 
(ii) 
(iii)  
( ii) ( iii) 
Question 2: 
If , then verify that 
(i) 
(ii)  
Answer We have: 
(i) 
(ii) 
and 
Question 3: 
If , then verify that  
(i) 
(ii) 
Answer 
(i) It is known that
Therefore, we have: 
and 
(ii)
Page 5


Exercise 3.3 
Question 1:  
Find the transpose of each of the following matrices: 
(i) 
Answer 
 (i) 
(ii) 
(iii)  
( ii) ( iii) 
Question 2: 
If , then verify that 
(i) 
(ii)  
Answer We have: 
(i) 
(ii) 
and 
Question 3: 
If , then verify that  
(i) 
(ii) 
Answer 
(i) It is known that
Therefore, we have: 
and 
(ii)
Question 4: 
If , then find 
Answer 
Question 5:  
For the matrices A and B, verify that (AB)' = where 
and 
We know that