In this post, you will find the complete NCERT Solutions for Maths Class 12 Exercise 3.1.
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NCERT Solutions for Maths Class 12 Exercise 3.2
NCERT Solutions for Maths Class 12 Exercise 3.3
NCERT Solutions for Maths Class 12 Exercise 3.4
NCERT Solutions for Maths Class 12 Exercise 3.1
Maths Class 12 Ex 3.1 Question 1.
In the
matrix
Write:
(i) The order of the matrix,
(ii) The number of elements,
(iii) Write the elements a13, a21, a33, a24,
a23.
Solution:
(i) The matrix A has 3 rows and 4
columns.
Therefore, the order of the matrix is 3 × 4.
(ii) There are 3 × 4 = 12 elements
in the matrix A.
(iii) In the given matrix, a13 =
19, a21 = 35, a33 = – 5, a24 =
12, a23 = 5/2
Maths Class 12 Ex 3.1 Question 2.
If a matrix has 24 elements, what are the possible orders it can have? What, if it has 13 elements?Solution:
We know that if a matrix is of order m × n, then it has mn elements.
(i) We have, 24 = 1 × 24 = 2 × 12 =
3 × 8 = 4 × 6
Thus, there are 8 matrices having 24 elements and their orders are (1 × 24),
(24 × 1), (2 × 12), (12 × 2), (3 × 8), (8 × 3), (4 × 6), (6 × 4).
(ii) We have, 13 = 1 × 13,
Thus, there are 2 matrices of 13 elements and their orders are (1 × 13) and (13
× 1).
Maths Class 12 Ex 3.1 Question 3.
If a matrix has 18 elements, what are the possible orders it can have ? What, if it has 5 elements.Solution:
We know that if a matrix is of order m × n, then it has mn elements.
(i) We have, 18 = 1 × 18 = 2 × 9 = 3
× 6
Thus, there are 6 matrices having 18 elements and their orders are (1 × 18), (18
× 1), (2 × 9), (9 × 2), (3 × 6), (6 × 3).
(ii) We have, 5 = 1 × 5
Thus, there are 2 matrices of 5 elements and their orders are (1 × 5) and (5 ×
1).
Maths Class 12 Ex 3.1 Question 4.
Construct a 2 × 2 matrix, A = [aij], whose elements are given by:
Solution:
Maths Class 12 Ex 3.1 Question 5.
Construct a 3 × 4 matrix, whose elements are given by:
Solution:
Maths Class 12 Ex 3.1 Question 6.
Find the values of x, y and z from the following equations:
Solution:
x² – 6x + 8 = 0
(x – 4)(x – 2) = 0
Therefore, x = 2, 4
When x = 2, y = 6 – 2 = 4 and when x = 4, y = 6 – 4 = 2
Hence, x = 2, y = 4, z = 0 or x = 4, y = 2, z = 0.
(iii) Equating
the corresponding elements, we get
x + y + z = 9 …..(i)
x + z = 5 ..…(ii)
y + z = 7 ..…(iii)
Adding equations (ii) and (iii), we get
x + y + 2z = 12
(x + y + z) + z = 12
9 + z = 12 [From equation (i)]
z = 3
x + z = 5
x + 3 = 5
Therefore, x = 2
From equation
(iii), y + z = 7
y + 3 = 7
y = 4
Hence, x = 2, y = 4 and z = 3.
Maths Class 12 Ex 3.1 Question 7.
Find the values of a,b,c and d from the equation:
Solution:
Equating the elements of both the matrices.
Maths Class 12 Ex 3.1 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:
For a square matrix, m = n.
Hence, option (C) is correct.
Maths Class 12 Ex 3.1 Question 9.
Which of the given values of x and y make the following pairs of matrices equal:
(B) Not possible to find
(C) y = 7, x = –2/3
(D) x = –1/3, y = –2/3
Solution:
(a) x = –1/3, y = 7
Maths Class 12 Ex 3.1 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:
The matrix is of order 3 × 3, therefore,
there are 9 entries in the matrix, each place can be filled with 0 or 1.
Then, 9 places can be filled in 29 =
512 ways
Thus, the number of such matrices = 512
Hence, option (D) is correct.
Related Links:
NCERT Solutions for Maths Class 12 Exercise 3.2