NCERT Solutions for CBSE Class 12 Mathematics ‒ Chapter 3: Matrices (Part II)

NCERT Solutions for CBSE 12th Maths, Chapter 3: Matrices are available here. In this article, you will find solutions of exercise 3.1 (from question number 6 to question number 10). These questions are mainly based on equality of Matrices. These questions are also important for CBSE Class 12 board exam 2018 and other engineering entrance exams.

Question 6:

Solution 6:

(i)

In the given matrix, if we compare the corresponding elements, x = 1, y = 4, and z = 3.

(ii)

In the given matrix, on comparing the corresponding elements, we have,

x + y = 6

⇒ xy = 8

⇒ 5 + z = 5 ⇒ z = 0

Now, (x − y)² = (x + y)² − 4xy

⇒ (x − y)² = 36 − 32 = 4

⇒ x − y = ±2

∴x = 4, y = 2, and z = 0 or x = 2, y = 4, and z = 0.

(iii)

Comparing the corresponding elements,

x + y + z = 9 … (1)

x + z = 5 …..... (2)

y + z = 7 …..... (3)

From …(1) and ….(2)

y + 5 = 9 ⇒ y = 4

Then, from (3) 4 + z = 7

⇒ z = 3 ∴ x + z = 5

⇒ x = 2

∴ x = 2, y = 4, and z = 3

NCERT Exemplar Class 12 Mathematics – Chapter 3: Matrics

Question 7:

Solution 7:

Comparing the corresponding elements,

a − b = −1 … (1)

2a − b = 0 … (2)

2a + c = 5 … (3)

3c + d = 13 … (4)

From equation …(2)

b = 2a

From (1), a − 2a = −1

⇒ a = 1 ⇒ b = 2

From (3), 2 ×1 + c = 5

⇒ c = 3

From equation (4), 3 ×3 + d = 13

⇒ 9 + d = 13

⇒ d = 4

∴ a = 1, b = 2, c = 3, and d = 4.

Question 8: A = [a_ij]m × n is a square matrix, if

(A) m < n

(B) m > n

(C) m = n

(D) None of these

Solution 8:

We know that, A given matrix is said to be a square matrix if the number of rows is equal to the number of columns. The correct answer is C.

A = [a_ij]_{m × n} is a square if m = n.

Question 9:

Solution 9:

On comparing the corresponding elements, we have,

3 x + 7 = 0

⇒ x = ‒7/3

Also, 5 = y ‒ 2 ⇒ y = 7

Again, y + 1 = 8

⇒ y = 7.

Also,

2 ‒ 3x = 4

⇒ x = ‒2/3.

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 10:

Elements of a 3 × 3 matrix = 9.

Each of these elements can be either 0 or 1.

Each of the 9 elements can be filled in two possible ways.

Therefore, by the multiplication principle, the required number of possible matrices is 2⁹ = 512.

Download NCERT Solutions for Class 12 Maths (Chapter 3 - Matrices) in PDF format