NCERT Solutions for Maths Class 12 Exercise 3.1

# NCERT Solutions for Maths Class 12 Exercise 3.1

NCERT Solutions for Maths Class 12 Exercise 3.1

## NCERT Solutions for Maths Class 12 Exercise 3.1

### Maths Class 12 Ex 3.1 Question 1.

In the matrix

Write:
(i) The order of the matrix,
(ii) The number of elements,
(iii) Write the elements a13, a21, a33, a24, a23.

Solution:
(i) The matrix A has 3 rows and 4 columns.
Therefore, the order of the matrix is 3 × 4.
(ii) There are 3 × 4 = 12 elements in the matrix A.
(iii) In the given matrix, a13 = 19, a21 = 35, a33 = – 5, a24 = 12, a23 = 5/2

### Maths Class 12 Ex 3.1 Question 2.

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

Solution:
We know that if a matrix is of order m × n, then it has mn elements.
(i) We have, 24 = 1 × 24 = 2 × 12 = 3 × 8 = 4 × 6
Thus, there are 8 matrices having 24 elements and their orders are (1 × 24), (24 × 1), (2 × 12), (12 × 2), (3 × 8), (8 × 3), (4 × 6), (6 × 4).
(ii) We have, 13 = 1 × 13,
Thus, there are 2 matrices of 13 elements and their orders are (1 × 13) and (13 × 1).

### Maths Class 12 Ex 3.1 Question 3.

If a matrix has 18 elements, what are the possible orders it can have ? What, if it has 5 elements.

Solution:
We know that if a matrix is of order m × n, then it has mn elements.
(i) We have, 18 = 1 × 18 = 2 × 9 = 3 × 6
Thus, there are 6 matrices having 18 elements and their orders are (1 × 18), (18 × 1), (2 × 9), (9 × 2), (3 × 6), (6 × 3).
(ii) We have, 5 = 1 × 5
Thus, there are 2 matrices of 5 elements and their orders are (1 × 5) and (5 × 1).

### Maths Class 12 Ex 3.1 Question 4.

Construct a 2 × 2 matrix, A = [aij], whose elements are given by:

Solution:

### Maths Class 12 Ex 3.1 Question 5.

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

### Maths Class 12 Ex 3.1 Question 6.

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

Clearly, 5 + z = 5, then z = 0

Again, x + y = 6 and xy = 8

y = 6 – x and x(6 – x) = 8
6x – x² = 8
x² – 6x + 8 = 0
(x – 4)(x – 2) = 0
Therefore, x = 2, 4
When x = 2, y = 6 – 2 = 4 and when x = 4, y = 6 – 4 = 2
Hence, x = 2, y = 4, z = 0 or x = 4, y = 2, z = 0.

(iii) Equating the corresponding elements, we get
x + y + z = 9           …..(i)
x + z = 5                 ..…(ii)
y + z = 7                 ..…(iii)
Adding equations (ii) and (iii), we get
x + y + 2z = 12
(x + y + z) + z = 12
9 + z = 12             [From equation (i)]
z = 3
x + z = 5
x + 3 = 5

Therefore, x = 2

From equation (iii), y + z = 7
y + 3 = 7
y = 4
Hence, x = 2, y = 4 and z = 3.

### Maths Class 12 Ex 3.1 Question 7.

Find the values of a,b,c and d from the equation:

Solution:
Equating the elements of both the matrices.

### Maths Class 12 Ex 3.1 Question 8.

A = [aij]m × n is a square matrix, if
(A) m < n              (B) m > n             (C) m = n               (D) None of these

Solution:
For a square matrix, m = n.
Hence, option (C) is correct.

### Maths Class 12 Ex 3.1 Question 9.

Which of the given values of x and y make the following pairs of matrices equal:

(A) x = –1/3, y = 7
(B) Not possible to find
(C) y = 7, x = –2/3
(D) x = –1/3, y = –2/3

(a) x = –1/3, y = 7

### Maths Class 12 Ex 3.1 Question 10.

The number of all possible matrices of order 3 × 3 with each entry 0 or 1 is
(A) 27
(B) 18
(C) 81
(D) 512

Solution:
The matrix is of order 3 × 3, therefore, there are 9 entries in the matrix, each place can be filled with 0 or 1.
Then, 9 places can be filled in 29 = 512 ways
Thus, the number of such matrices = 512
Hence, option (D) is correct.