## CONSTRUCT A MATRIX WITH GIVEN ORDER

Construct a Matrix With Given Order :

In this section, you will learn how to construct a matrix with the order given.

## Constructing a Matrix With Given Order - Practice Questions

Question 1 :

Construct an m × n matrix A  =  [aij], where aij is given by

(i)  aij  =  (i - 2j)2/2 with m = 2 and n = 3

Solution :

In general, a 2 x 3 is given by A =

General term :

aij  =  (i - 2j)2/2

 i = 1 and j = 1a11 = (1 - 2)2/2  =  (-1)2/2  =  1/2 i = 1 and j = 2a12  =  (1 - 4)2/2  =  (-3)2/2  =  9/2 i = 1 and j = 3a13  =  (1 - 6)2/2  =  (-5)2/2  =  25/2 i = 2 and j = 1a21 = (2 - 2)2/2  =  0/2 =  0 i = 2 and j = 2a21 = (2 - 4)2/2  =  4/2 =  2 i = 2 and j = 3a21 = (2 - 6)2/2  =  16/2 =  8

Hence the required matrix with order 2 x 3 is

(ii)  aij  =  |3i - 4j|/4 with m = 3 and n = 4

Solution :

In general, a .3 x 4 is given by A =

General term :

aij  = |3i - 4j|/4

## Elements of First Row

 i = 1 and j = 1aij  = |3i - 4j|/4a11  =  |3 - 4|/4=  1/4 i = 1 and j = 2aij  = |3i - 4j|/4a12  =  |3 - 8|/4=  5/4 i = 1 and j = 3aij  = |3i - 4j|/4a12  =  |3 - 12|/4=  9/4 i = 1 and j = 4aij  = |3i - 4j|/4a12  =  |3 - 16|/4=  13/4

## Elements of Second Row

 i = 2 and j = 1aij  = |3i - 4j|/4a21  =  |6 - 4|/4=  2/4 = 1/2 i = 2 and j = 2aij  = |3i - 4j|/4a21  =  |6 - 8|/4=  2/4 = 1/2 i = 2 and j = 3aij  = |3i - 4j|/4a21  =  |6 - 12|/4=  6/4 = 3/2 i = 2 and j = 4aij  = |3i - 4j|/4a21  =  |6 - 16|/4=  10/4 = 5/2

## Elements of Third Row

 i = 3 and j = 1aij  = |3i - 4j|/4a31  =  |9 - 4|/4=  5/4 i = 3 and j = 2aij  = |3i - 4j|/4a32  =  |9 - 8|/4=  1/4 i = 3 and j = 3aij  = |3i - 4j|/4a33  = |9 - 12|/4=  3/4 i = 3 and j = 4aij  = |3i - 4j|/4a34  = |9 - 16|/4=  7/4

Hence the required matrix with order 3 x 4 is

After having gone through the stuff given above, we hope that the students would have understood how to construct a matrix with the order given

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