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)3/3

a13  =  64/3


 a21  = (2+1)3/3

  =  27/3

 a21  =  9

 a22 = (2+2)3/3

 =  64/3

 a22  =  64/3

 a23 = (2+3)3/3

a23  =  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)3/3

a33  =  216/3


Hence the required matrix is 

After having gone through the stuff given above, we hope that the students would have understood, "How to Find the Number of Elements in a Matrix". 

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