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 = 1

a11 = (1 - 2)2/2

  =  (-1)2/2 

=  1/2

i = 1 and j = 2

a12  =  (1 - 4)2/2

  =  (-3)2/2

  =  9/2

i = 1 and j = 3

a13  =  (1 - 6)2/2

  =  (-5)2/2

  =  25/2

i = 2 and j = 1

a21 = (2 - 2)2/2

  =  0/2 

=  0

i = 2 and j = 2

a21 = (2 - 4)2/2

  =  4/2 

=  2

i = 2 and j = 3

a21 = (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 = 1

aij  = |3i - 4j|/4

a11  =  |3 - 4|/4

=  1/4

i = 1 and j = 2

aij  = |3i - 4j|/4

a12  =  |3 - 8|/4

=  5/4

i = 1 and j = 3

aij  = |3i - 4j|/4

a12  =  |3 - 12|/4

=  9/4

i = 1 and j = 4

aij  = |3i - 4j|/4

a12  =  |3 - 16|/4

=  13/4

Elements of Second Row

i = 2 and j = 1

aij  = |3i - 4j|/4

a21  =  |6 - 4|/4

=  2/4 = 1/2

i = 2 and j = 2

aij  = |3i - 4j|/4

a21  =  |6 - 8|/4

=  2/4 = 1/2

i = 2 and j = 3

aij  = |3i - 4j|/4

a21  =  |6 - 12|/4

=  6/4 = 3/2

i = 2 and j = 4

aij  = |3i - 4j|/4

a21  =  |6 - 16|/4

=  10/4 = 5/2

Elements of Third Row

i = 3 and j = 1

aij  = |3i - 4j|/4

a31  =  |9 - 4|/4

=  5/4 

i = 3 and j = 2

aij  = |3i - 4j|/4

a32  =  |9 - 8|/4

=  1/4 

i = 3 and j = 3

aij  = |3i - 4j|/4

a33  = |9 - 12|/4

=  3/4 

i = 3 and j = 4

aij  = |3i - 4j|/4

a34  = |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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