Class 12 Maths

# Matrices

## NCERT Solution

### Exercise 1 Part 2

Question 5: Construct a 3 x 4 matrix, whose elements are given by

**Answer:**

Question: 6 – Find the values of x, y and z from the following equations:

**Answer:** Here, it is clear that, x = 1; y = 4 and z = 3

**Solution:**

**Solution:**

From equation (i) and (ii) we get

After substituting the value of y in equation (iii) we get

After substituting the value of z in equation (ii) we get

Question: 7 – Find the values of a, b, c and d from the equations:

**Solution:**

From equation (i) and (ii) we get

After substituting the value of a in equation (i) we get

After substituting the value of a in equation (iii) we get

After substituting the value of c in equation (iv) we get

Question 8: is a square matrix if:

(A) m < n

(B) n > n

(C) m = n

(D) None of these

**Solution:** (C) m = n

Explanation: When the number of column is equal to number of row, then matrix is a square matrix. Therefore, option (C) m = n is correct.

Question 9: Which of the given values of x and y make the following pair of matrices equal?

**Solution:** (B) Not possible to find

Explanation:

Here, x has two values which is not possible, because x can have only one value at a time. Thus, given matrices can never be equal. Thus, option ‘(B) Not possible to find’ is correct.

Question 10: The number of all possible matrices of order 3 x 3 with each entry 0 or 1 is:

(A) 27

(B) 18

(C) 81

(D) 512

**Solution:** (D) 512

Explanation: Given matrices is of 3 x 3 order.

This means the given matrices has 3 x 3 = 9 elements.

As given, there are two options for entry, i.e. 0 and 1.

Thus, number of possible matrices = (2)^{9} = 512

Hence, option ‘(D) 512’ is correct.

Exercise 3.1

Exercise 3.2