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NCERT Solutions Class 12 Maths Chapter 3 - Matrices

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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 
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FAQs on NCERT Solutions Class 12 Maths Chapter 3 - Matrices

1. What is a matrix?
Ans. A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. In other words, it is a collection of numbers arranged in a specific order.
2. How can we add two matrices?
Ans. To add two matrices, we have to add the corresponding elements of both the matrices. For example, if we have two matrices A and B, then the sum of A and B will be a matrix C, where Cij = Aij + Bij (where i represents the row number and j represents the column number).
3. What is a scalar matrix?
Ans. A scalar matrix is a square matrix in which all the elements of the main diagonal are equal, and all the other elements are zero. In other words, a scalar matrix is a matrix in which each element is a scalar multiple of the identity matrix. For example, the matrix [2 0; 0 2] is a scalar matrix.
4. Can we multiply two matrices of different sizes?
Ans. No, we cannot multiply two matrices of different sizes. In order to multiply two matrices, the number of columns in the first matrix should be equal to the number of rows in the second matrix. If the matrices have different sizes, then they cannot be multiplied.
5. What is the transpose of a matrix?
Ans. The transpose of a matrix is obtained by interchanging its rows and columns. In other words, if A is a matrix of size m x n, then the transpose of A is a matrix of size n x m, denoted by A^T, in which the element in the ith row and jth column of A becomes the element in the jth row and ith column of A^T. For example, if A = [1 2 3; 4 5 6], then A^T = [1 4; 2 5; 3 6].
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