NCERT Solutions Class 12th Maths Chapter 3 – Matrices Exercise 3.1

NCERT Solutions Class 12th Maths Chapter 3 – Matrices Exercise 3.1

NCERT Solutions Class 12th Maths Chapter 3 – Matrices Exercise 3.1

?Chapter – 3?

✍Matrices✍

?Exercise 3.1?

1.In the matrix A = 

The order of the matrix

Solution: In the given matrix, the number of rows is 3 and the number of columns is 4. Therefore, the order of the matrix is 3 × 4.

ii). In the matrix A = 

The number of elements,

Solution: Since the order of the matrix is 3 × 4, there are 3 × 4 = 12 elements in it.

3. Let 

Find A – B

Solution:

iii)  Write the elements a₁₃, a₂₁, a₃₃, a₂₄, a₂₃

Solution: a₁₃ = 19, a₂₁ = 35, a₃₃ = −5, a₂₄ = 12, a₂₃ = 5/2

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

Solution: We know that if a matrix is of the order m × n, it has mn elements. Thus, to find all the possible orders of a matrix having 24 elements, we have to find all the ordered pairs of natural numbers whose product is 24.
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
(1, 13) and (13, 1) are the ordered pairs of natural numbers whose product is 13.
Hence, the possible orders of a matrix having 13 elements are 1 × 13 and 13 × 1.

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 the order m × n, it has mn elements. Thus, to find all the possible orders of a matrix having 18 elements, we have to find all the ordered pairs of natural numbers whose product is 18.
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
(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.

5. Construct a 2 × 2 matrix, whose elements are given by:

Solution:

In general, a 2 × 2 matrix is given by

 i, j = 1, 2

Therefore, the required matrix is 

ii. Construct a 2 × 2 matrix, whose elements are given by

Solution:

In general, a 2 × 2 matrix is given by A =

Therefore, the required matrix is A =

iii. Construct a 2 × 2 matrix,  whose elements are given by:

Solution:

In general, a 2 × 2 matrix is given by A =

Therefore, the required matrix is

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

Solution:

In general, a 3 × 4 matrix is given by A=

a_(ij) = 1/2 |-3i + j|, i = 1,2,3 and j =  1,2 ,3,4

Therefore, the required matrix is A =

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

Solution:

In general, a 3 × 4 matrix is given by

Therefore, the required matrix is

12. Construct a 2 × 2 matrix, whose elements are given by

Solution:

In general, a 2 × 2 matrix is given by A =

Therefore, the required matrix is

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

Solution:

In general, a 3 × 4 matrix is given by

a_(ij) = 1/2 |-3i + j|, i = 1,2,3 and j =  1,2 ,3,4

Therefore, the required matrix is A =