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 = [aij]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 = [aij]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
