Test: Introduction To Matrices - JEE MCQ

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).

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.

= x+10 = 3x+4
= x = 3

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

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.

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. 

There are 2 rows and 5 columns in the matrix.
Therefore, order of the matrix: 2 x 5.

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

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.

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.

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.