# EXERCISE 3.1 (MATRIX)

Class 12 ncert solution math exercise 3.1 matrix

Question 1: (i) The order of the matrix

(ii) The number of elements

(iii) Write the elements

Solution: (i) Since, in the given matrix, the number of rows is 3 and the number of columns is 4 , the order of the matrix is .

(ii) Since the order of the matrix is , there are elements.

(iii) Here,

Question 2: Â 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 , it has 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: and .

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

and are the ordered pairs of natural numbers whose product is 13 . Hence, the possible orders of a matrix having 13 elements are and .

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

Solution: We know that if a matrix is of the order , it has 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: and .

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

and are the ordered pairs of natural numbers whose product is 5 .

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

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

(i)

(ii)

(iii)

Solution: In general, a matrix is given by

(i)

Therefore,

(ii)

Therefore,

Thus, the required matrix is

(iii)

Therefore,

Thus, the required matrix is

Question 5: In general, a matrix whose elements are given by

(i)

(ii)

Solution:Â

(i) Given

Thus, the required matrix is

(ii)

Thus, the required matrix is

Question 6: Find the value of and from the following equation:
(i)

(ii)

(iii)

Solution: (i)

As the given matrices are equal, their corresponding elements are also equal.

Comparing the corresponding elements, we get:

(ii)

As the given matrices are equal, their corresponding elements are also equal.

Comparing the corresponding elements, we get:

Hence,

We know that

Equating and , we get

Similarly, Equating and , we get

Thus, or

(iii)

As the given matrices are equal, their corresponding elements are also equal.

Comparing the corresponding elements, we get:

From (1) and (2), we have

From (3), we have

Therefore,

Thus,

Question 7: Find the value of and from the equation:

Solution:

As the two matrices are equal, their corresponding elements are also equal.

Comparing the corresponding elements, we get:

From (2),

Putting this value in (1),

Hence,

Putting
in (3),

Putting in ,

Thus, and .

Question 8: is a square matrix, if
(A)
(B)
(C)
(D) None of these

Solution: It is known that a given matrix is said to be a square matrix if the number of rows is equal to the number of columns.

Therefore, is a square matrix, if .

Thus, the correct option is {C}.

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

(A)
(B) Not possible to find
(C)
(D)

Solution: The given matrices are and

Equating the corresponding elements, we get:

We find that on comparing the corresponding elements of the two matrices, we get two different values of , which is not possible.

Hence, it is not possible to find the values of and for which the given matrices are equal.

Thus, the correct option is .

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

(A) 27
(B) 18
(C) 81
(D) 512

Solution: The given matrix of the order has 9 elements and each of these elements can be either 0 or 1 .

Now, each of the 9 elements can be filled in two possible ways.

Hence, by the multiplication principle, the required number of possible matrices is .

Thus, the correct option is D.