Class 12 Maths

Matrices

NCERT Solution

Exercise 1 Part 2

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

class 12 math matrices ncert exercise 3.1-8

Answer:

class 12 math matrices ncert exercise 3.1-9
class 12 math matrices ncert exercise 3.1-10 class 12 math matrices ncert exercise 3.1-10A
class 12 math matrices ncert exercise 3.1-11 class 12 math matrices ncert exercise 3.1-11A
class 12 math matrices ncert exercise 3.1-12 class 12 math matrices ncert exercise 3.1-12A
class 12 math matrices ncert exercise 3.1-13 class 12 math matrices ncert exercise 3.1-13A
class 12 math matrices ncert exercise 3.1-14 class 12 math matrices ncert exercise 3.1-14A
class 12 math matrices ncert exercise 3.1-15 class 12 math matrices ncert exercise 3.1-15A
class 12 math matrices ncert exercise 3.1-16 class 12 math matrices ncert exercise 3.1-16A
class 12 math matrices ncert exercise 3.1-17 class 12 math matrices ncert exercise 3.1-17A
class 12 math matrices ncert exercise 3.1-18 class 12 math matrices ncert exercise 3.1-18A
class 12 math matrices ncert exercise 3.1-19 class 12 math matrices ncert exercise 3.1-19A
class 12 math matrices ncert exercise 3.1-20 class 12 math matrices ncert exercise 3.1-20A
class 12 math matrices ncert exercise 3.1-21 class 12 math matrices ncert exercise 3.1-21A
class 12 math matrices ncert exercise 3.1-22
class 12 math matrices ncert exercise 3.1-23
class 12 math matrices ncert exercise 3.1-24

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

class 12 math matrices ncert exercise 3.1-25

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

class 12 math matrices ncert exercise 3.1-26

Solution:

class 12 math matrices ncert exercise 3.1-27
class 12 math matrices ncert exercise 3.1-28

Solution:

class 12 math matrices ncert exercise 3.1-29

From equation (i) and (ii) we get

class 12 math matrices ncert exercise 3.1-30

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

class 12 math matrices ncert exercise 3.1-31

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

class 12 math matrices ncert exercise 3.1-32

Question: 7 – Find the values of a, b, c and d from the equations: class 12 math matrices ncert exercise 3.1-33

Solution:

class 12 math matrices ncert exercise 3.1-34

From equation (i) and (ii) we get

class 12 math matrices ncert exercise 3.1-35

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

class 12 math matrices ncert exercise 3.1-36

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

class 12 math matrices ncert exercise 3.1-37

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

class 12 math matrices ncert exercise 3.1-38

Question 8: class 12 math matrices ncert exercise 3.1-39 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?

class 12 math matrices ncert exercise 3.1-40
class 12 math matrices ncert exercise 3.1-41

Solution: (B) Not possible to find

Explanation:

class 12 math matrices ncert exercise 3.1-42

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