# NCERT Solutions for CBSE Class 12 Mathematics ‒ Chapter 3: Matrices (Part I)

NCERT Solutions for CBSE Class 12th Mathematics, Chapter 3: Matrices are available here. Here, you will find solutions of exercise 3.1 (from question number 1 to question number 5). These questions are based on types of matrices and equality of Matrices. These questions are also important for CBSE Class 12 board exam 2018 and other engineering entrance exams.

*NCERT Solutions for CBSE Class 12th Maths, Chapter 3: Matrices (Exercise 3.1) are given below*

**Question 1:**

**Solution 1:**

(*i*) Number of rows = 3; Number of columns = 4

Thus, the order of the matrix = 3 × 4

(*ii*) Order of the matrix = 3 × 4

Thus, no. of elements = 3 × 4 = 12

(*iii*) *a*_{13} = 19

*a*_{21} = 35

*a*_{33} = −5

*a*_{24} = 12

**NCERT Exemplar Class 12 Mathematics – Chapter 3: Matrics**

**Question 2:**

If a matrix has 24 elements, what are the possible orders it can have? What, if it has 13 elements?

**Solution 2:**

Order of a matrix = *m* × *n*

Then, no. of elements will be = *mn *elements

Orders of a matrix having 24 elements are:

The ordered pairs are: (1, 24), (24, 1), (2, 12), (12, 2), (3, 8), (8, 3), (4, 6), and (6, 4)

Hence, the possible orders of a matrix having 24 elements are:

1 × 24, 24 × 1, 2 × 12, 12 × 2, 3 × 8, 8 × 3, 4 × 6, and 6 × 4

Orders of a matrix having 13 elements are:

Order pairs = (1, 13) and (13, 1)

Hence, the possible orders of a matrix having 13 elements are 1 × 13 and 13 × 1.

**Question 3:**

If a matrix has 24 elements, what are the possible orders it can have? What, if it has 13 elements?

**Solution 3:**

Order of a matrix = *m* × *n*

Then, no. of elements will be = *mn* elements

Orders of a matrix having 18 elements are:

The ordered pairs are: (1, 18), (18, 1), (2, 9), (9, 2), (3, 6,), and (6, 3)

Hence, the possible orders of a matrix having 18 elements are:

1 × 18, 18 × 1, 2 × 9, 9 × 2, 3 × 6, and 6 × 3

Orders of a matrix having 5 elements are:

(1, 5) and (5, 1) are the ordered pairs of natural numbers whose product is 5

Hence, the possible orders of a matrix having 5 elements are 1 × 5 and 5 × 1.

**Question 4:**

Construct a 2 × 2 matrix, A = [a_{ij}], whose elements are given by:

(*i*) a_{ij} = (*i* + *j*)^{2}/2

(*ii*) a_{ij} = *i*/*j*

(*iii*) a_{ij} = (*i* + 2*j*)^{2}/2

**Solution 4:**

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**Question 5:**

Construct a 3 × 4 matrix, whose elements are given by:

(*i*) *a*_{ij }= (1/2) |-3*i* + *j* |

(*ii*) *a*_{ij} = 2*i* - *j*

**Solution 5:**

**Download NCERT Solutions for Class 12 Maths (Chapter 3 - Matrices) in PDF format**