Class 12 Maths

# Matrices

## NCERT Solution

### Exercise 1 Part 1

Question 1: In the matrix write:

(i) The order of the matrix,

(ii) The number of elements,

(iii) Write the elements a_{13}, a_{21}, a_{33}, a_{24}, a_{23}.

**Solution:**

(i) Since, the given matrix A has three rows and four columns, thus, order of the matrix = 3 x 4

(ii) The given matrix A has 3 x 4 = 12 elements

(iii) a_{13} = 19, a_{21} = 35, a_{33} = –5, a_{24} = 12, a_{23} = 5/2.

Question -2 – If a matrix has 24 elements, what are the possible orders it can have? What if it has 13 elements.

**Solution:** Since, a matrix is of order m x n has mn elements, thus, possible orders of the having 24 elements will be 1 x 24, 2 x 12, 3 x 8, 4 x 6, 6 x 4, 8 x 3, 12 x 2 and 24 x 1.

Matrix having 13 elements has possible orders are 1 x 13 and 13 x 1

Question: 3 – If a matrix has 18 elements, what are the possible orders it can have? What, if it has 5 elements?

**Solution:** Possible orders of matrix having 18 elements are 1 x 18, 2 x 9, 3 x 6, 6 x 3, 9 x 2, 18 x 1.

Similarly, possible orders of a matrix having 5 elements are 1 x 5 and 5 x 1

Question 4: Construct a whose elements are given by:

**Solution:**