# HOW TO FIND THE NUMBER OF ELEMENTS IN A MATRIX

How to Find the Number of Elements in a Matrix ?

Here we are going to see how to find the number of elements in a matrix.

## How to Find the Number of Elements in a Matrix - Practice Questions

Question 1 :

In the matrix A =

write (i) The number of elements

(ii) The order of the matrix (iii) Write the elements a22, a23 , a24 , a34, a43 , a44.

Solution :

(i)  In the given matrix, we have 4 rows and 4 columns.

Hence the number of elements in the given matrix is 16.

(ii)  The order of matrix is 4 x 4.

(iii)  a22 means the element is in place 2nd row and second column.

a22  =  √7

a23  =  √3/2 (Element at the 2nd row and 3rd column)

a24  =  5 (Element at the 2nd row and 4th column)

a34  =  0 (Element at the 3rd row and 4th column)

a43  =  -11 (Element at the 4th row and 3rd column)

a44  =  1 (Element at the 4th row and 4th column)

Question 2 :

If a matrix has 18 elements, what are the possible orders it can have? What if it has 6 elements?

Solution :

Possible orders of matrices having 18 elements are 1 x 18, 18 x 1, 6 x 3, 3 x 6 , 2 x 9, 9 x 2.

Possible orders of matrices having 6 elements are 1 x 6, 6 x 1, 2 x 3, 3 x 2.

## How to Construct a Matrix with Given aij

Question 1 :

Construct a 3 x 3 matrix whose elements are given by

(i)  aij  =  |i - 2j|

Solution :

Number of rows of the required matrix is 3.

Number of columns of the required matrix is 3.

 aij  =  |i - 2j|a11  =  |1 - 2(1)|  =  |1 - 2| a11  =  1 aij  =  |i - 2j|a12  =  |1 - 2(2)|  =  |1 - 4| a12  =  3 aij  =  |i - 2j|a13  =  |1 - 2(3)|  =  |1 - 6| a11  =  5
 a21 = |2 - 2(1)|  =  |2 - 2| a21  =  0 a22 = |2 - 2(2)|  =  |2 - 4| a22  =  2 a23 = |2- 2(3)|  =  |2 - 6| a23  =  4
 a31 = |3 - 2(1)|  =  |3 - 2| a31  =  1 a32 = |3 - 2(2)|  =  |3 - 4| a32  =  1 a33 = |3- 2(3)|  =  |3 - 6| a33  =  3

Hence the required matrix is A  =

(ii)   aij  =  (i + j)3/3

 aij  =  (i + j)3/3 a11  =  (1+1)3/3  =  23/3 a11  =  8/3 aij  =  (i + j)3/3 a12 = (1+2)3/3 =  27/3 a12  =  9 aij  =  (i + j)3/3 a13 = (1+3)3/3a13  =  64/3
 a21  = (2+1)3/3  =  27/3 a21  =  9 a22 = (2+2)3/3 =  64/3 a22  =  64/3 a23 = (2+3)3/3a23  =  125/3
 a31  = (3+1)3/3  =  64/3 a31  =  64/3 a32 = (3+2)3/3 =  125/3 a32  =  125/3 a33 = (3+3)3/3a33  =  216/3

Hence the required matrix is

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