Test: Introduction To Matrices

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

Since, there are 2 rows and 2 columns in the matrix, order of the matrix is 2*2.

The number of elements in a 2 x 2 matrix is the product 2 x 2 =4

Each element can either be a 0,1 or 2.

Given this, the total possible matrices that can be selected is 3⁴

3^2x2= 3⁴= 81

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

a_ij = 1/2 |i-3j|
As a_ij = a₂₂ ie i = 2 and j = 2
By substituting the values in the equation, we get
a₂₂ = 1/2 |2-3(2)| = 1/2 |-4| = 2 

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.

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.