Chapter 3 Matrices Ex 3.1 Solutions
Question - 1 : - 
Answer - 1 : -
Question - 2 : - If a matrix has 24 elements, whatare possible orders it can order? What, if it has 13 elements?
Answer - 2 : -
Since, a matrix having 
elementis of order 
(i) Therefore, there are 8 possible matrices having 24elements of orders
1 x 24, 2 x 12, 3 x 8, 4 x 6, 24 x 1, 12 x 2, 8 x 3, 6 x 4.
(ii) Prime number 13 = 1 x 13 and 13 x 1
Therefore, there are 2 possible matrices of order 1 x 13(Row matrix) and 13 x 1 (Column matrix).
Question - 3 : - If a matrix has 18 elements, whatare the possible orders it can have? What if has 5 elements?
Answer - 3 : -
Since, a matrix having elementis of order
(i) Therefore, there are 6 possible matrices having 18elements of orders 1 x 18, 2 x 9, 3 x 6, 18 x 1, 9 x 2, 6 x 3.
(ii) Prime number 5 = 1 x 5 and 5 x 1
Therefore, there are 2 possible matrices of order 1 x 5 (Rowmatrix) and 5 x 1 (Column matrix).
Question - 4 : - Construct a 2 x 2 matrix A = 
whoseelements are given by:
Answer - 4 : -
(i)
(ii)
(iii) 
Solution
(i) Given: ……….(i)
Putting 
ineq. (i) 
Putting 
ineq. (i) 
Putting 
ineq. (i) 
Putting 
ineq. (i) 
A2x 2 = 
(ii) Given: ……….(i)
Putting ineq. (i) 
Putting ineq. (i) 
Putting ineq. (i) 
Putting ineq. (i) 
A2x 2 = 
(iii) Given: ……….(i)
Putting ineq. (i) 
Putting ineq. (i) 
Putting ineq. (i)
Putting ineq. (i) 
A2 x 2 = 
Question - 5 : - Constructa 3 x 4 matrix, whose elements are given by:
Answer - 5 : -
(i) 
(ii) 
Solution
(i) Given: ……….(i)
Putting ineq. (i) 
Putting ineq. (i)
Question - 6 : - Findthe values of 
and 
fromthe following equations:
Answer - 6 : -
(i) 
(ii) 
(iii) 
Solution
(i)Given:
By definition of Equal matrices, 
(ii)
Equating corresponding entries, 
……….(i)
……….(ii)
And 
[Fromeq. (i), 
or 
Putting these values of 
ineq. (i), we have 
and 
or x = 4, y=2, z=0
(iii) Given: Equating corresponding entries, 
……….(i)
………. (ii)
And 
……….(iii)
9 – 5 = 4Eq. (i) – Eq. (iii) = 
9– 7 = 2
Putting values of and 
in eq. (i),
Question - 7 : - Find the values of 
and 
fromthe equation 
.
Answer - 7 : -
Equating corresponding entries,
……….(i)
……….(ii)
……….(iii)
……….(iv)
Eq. (i) – Eq. (ii) = 
Putting 
ineq. (i), 
Putting ineq. (iii), 
Putting 
ineq. (iv), 
Question - 8 : - A = 
isa square matrix if:
Answer - 8 : -
(A) 
(B) 
(C) 
(D)None of these
Solution
By definition of square matrix ,option (C) is correct.
Question - 9 : - Which of the given values of and makethe following pairs of matrices equal:
Answer - 9 : - 
(A) 
(B) Not possible to find
(C) 
(D) 
Solution
Equating corresponding sides,
And 
Also 
And 
Since, values of arenot equal, therefore, no values of and existto make the two matrices equal.
Therefore, option (B) is correct.
The number of all possible matricesof order 3 x 3 with each entry 0 or 1 is:
Answer - 10 : -
(A) 27 (B) 18
(C) 81 (D) 512
Solution
Since, general matrix of order 3 x 3is 
This matrix has 9 elements.
The number of choices for 
is 2 (as 0 or 1 can be used)
Similarly, the number of choices for each other element is 2.
Therefore, total possible arrangements(matrices) = 
times= 
Therefore, option (D) is correct.