HOW TO FIND THE NUMBER OF ELEMENTS IN A MATRIX

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 , a_44.

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.

a_{22  =}  √7

a_23  =  √3/2 (Element at the 2^nd row and 3^rd column)

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

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

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

a₄₄  =  1 (Element at the 4^th row and 4^th 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 3 :

Construct a 3 x 3 matrix whose elements are given by

(i)  a_ij  =  |i - 2j|

Solution :

Number of rows of the required matrix is 3.

Number of columns of the required matrix is 3.

Hence the required matrix is A  =

(ii)   a_ij  =  (i + j)³/3

Solution :

Hence the required matrix is 

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