Matrices Test

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Matrices Test - 4

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Weekly Quiz Competition

Question 1
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Which of the following is a matrix of the order 2 ×2 where the equation of the elements is given by a_ij =i+j.

A

B

C

D

Solution
Question 2
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What is the order of the matrix A =

A
2 ×3

B
2 ×2

C
3 ×3

D
4 ×4

Solution

The number of rows (m) and the number of columns (n) in the given matrix A=

is 2. Therefore, the order of the matrix is 2 ×2(m ×n).
Question 3
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If the order of the matrix is m ×n, then how many elements will there be in the matrix?

A
mn

B
m² n²

C
mn²

D
2mn

Solution

The number of elements for a matrix with the order m ×n is equal to mn, where m is the number of rows and n is the number of columns in the matrix.
Question 4
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Then the value of x is ____

A
6

B
3

C
2

D
0

Solution

= x+10 = 3x+4
= x = 3
Question 5
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The number of all possible matrices of order 2 ×2 with each entry 0 or 1 is:

A
27

B
18

C
16

D
81

Solution

The number of possible entries of 2 ×2 matrix is 4 Every entry has two choice, 0 or 1.
Thus, the total no. of choices is,
2 ×2 ×2 ×2 = 2⁴
= 16
Question 6
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Let A and B be two non zero square matrics and AB and BA both are defined. It means

A
No. of columns of A ≠No. of rows of B

B
No. of rows of A ≠No. of columns of B

C
Both matrices (A) and (B) have same order

D
Both matrices (A) and (B) does not have same order

Solution

Given:
A and B be two non zero square matrics
Calculations:
Matrix AB is defined means Columns is equal to the Rows of B
and BA is defined means Columns of B is equal to the Rows of A
Hence, Both matrices (A) and (B) have same order is Correct.
Question 7
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is example of:

A
An identity matrix

B
A zero matrix.

C
A Scalar m

D
Diagonal matrix.

Solution

A matrix having non-zero elements only in the diagonal running from the upper left to the lower right.
The given matrix is a diagonal matrix.
Question 8
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is a matrix of order

A
2 x 5

B
2 x 2

C
5 x 2

D
5 x 5

Solution

There are 2 rows and 5 columns in the matrix.
Therefore, order of the matrix: 2 x 5.
Question 9
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What is the element in the 2^nd row and 1^st column of a 2 x 2 Matrix A = [ a_ij ], such that a = (i + 3) (j –1)?

A
0

B
4

C
-5

D
5

Solution

Rows are represented by i
Columns are represented by j
^{._. .} a = (i+3)(j-1)
i = 2 , j = 1 (given)
a₂₁ = (2+3)(1-1) = 0
so, a₂₁ = 0
Question 10
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If A is a matrix of order 3 ×5 and B is a matrix of order 5 ×3, then the order of AB and BA will respectively b
A
3 ×3 and 3 ×3

B
3 ×5 and 5 ×3

C
3 ×3 and 5 ×5

D
5 ×3 and 3 ×5

Solution

Calculation:
Given: A is a matrix of order 3 ×5 and B is a matrix of order 5 ×3
Number of rows in A = 3
Number of column in A = 5
Number of rows in B = 5
Number of column in B = 3
The order of AB = number of row is A ×number of columns in B
= 3 ×3
And,
The order of BA = number of row is B ×number of columns in A
= 5 ×5
Hence, option (3) is correct.
Question 11
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Consider the following information regarding the number of men and women workers in three factories I. II and III
What does the entry in the third row and second column represent if the information is represented as a 3 x 2 matrix?

A
The number of Men in factory I.

B
The number of Women in factory III.

C
The number of Women in factory II.

D
The number of Men in III.

Solution

The information is represented in the form of a 3 X 2 matrix as follows:
The entry in the third row and second column represents the number of women workers in factory III.
Question 12
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Which of the following is not a possible ordered pair for a matrix with 6 elements?

A
(2,3)

B
(3,2)

C
(1,6)

D
(3,1)

Solution

The possible orders in which the matrix with 6 elements can be formed are 2 ×3, 3 ×2, 1 ×6, 6 ×1.
Therefore, the possible orders pairs are (2,3), (3,2), (1,6), (6,1).
Thus, (3,1) is not possible.
Therefore, the correct answer is D.