**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:** **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: **

**(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.**