CPNM LAB PROGRAM-12

 

12. Write a function which will invert a matrix.

FLOW CHART

Algorithm: 

Step – 1 : Start 

Step – 2 : Declare array a[10][10], variables i, j, n 

Step – 3 : Print enter order of matrix 

Step – 4 : Initialize i to zero 

Step – 5 : Check whether i < n if true go to next Step and execute from Step–9 otherwise increment i by 1 

Step – 6 : Initialize j to zero 

Step – 7 : Check whether j < n if true execute Step–8 and Step–9 otherwise increment i by 1and go to Step–5 

 Step – 8 : Read elements into an array 

Step – 9 : Increment j by 1 and go to Step–7 

Step – 10 : Call function inverse(a, n) 

Step – 11 : Declare variables I, j, k array b[10][10] 

Step – 12 : Initialize i to zero 

Step – 13 : Check whether i < n if true execute from Step–14 to Step–19 otherwise go to Step–20 Step – 14 : Initialize j to zero 

Step – 15 : Check whether j < n if true execute Step–16 and Step–17 otherwise go to Step–18 

Step – 16 : Calculate b[i][j] = 0.0 

Step – 17 : Increment j by 1 and go to Step–13 

Step – 18 : b[i][i] = 1.0 

Step – 19 : Increment i by 1 and go to Step–13 

Step – 20 : Initialize k =0 

Step – 21 : Check whether k < n if true execute from Step–22 to Step–31 otherwise go to Step–30 Step – 22 : Initialize i to zero 

Step – 23 : Check whether i < n if true executes from Step–24 to Step–31 otherwise go to Step–21 by increment k by 1 

Step – 24 : Check whether i == k if true go to Step–21 otherwise go to Step–25 

Step – 25 : Calculate r = a[i][k] / a[k][k] 

Step – 26 : Initialize j to zero 

Step – 27 : Check whether j is less than if true execute from Step–28 to Step–30 otherwise go to Step–23 by i + 1 

 Step – 28 : Calculate a[i][j] -=r * a[k][j] 

 Step – 29 : Calculate a[i][j] -=r * b[k][j] 

Step – 30 : Increment j by 1 and go to Step–27 

Step – 31 : Initialize i to zero 

Step – 32 : Check whether i < n if true execute from Step–33 to Step–36 otherwise go to Step–37 Step – 33 : Initialize j to zero 

Step – 34 : Check whether j < n if true execute Step–35 and Step–36 otherwise go to Step–32 by incrementing i by 1 

Step – 35 : Calculate b[i][j] = a[i][j] / a[i][i] 

Step – 36 : Increment j by 1 and go to Step–34 

 Step – 37 : Initialize i to zero 

Step – 38 : Check whether i < n if true execute from Step–39 to Step–42 otherwise return to main Step – 39 : Initialize j to zero 

Step – 40 : Check whether j < n if true execute Step–40 and Step–41 otherwise increment  

                   i by 1 and go to Step - 38 

Step – 41 : Print b[i][j] 

Step – 42 : Increment j by 1 and go to Step–39 

Step – 43 : Stop 

Program:

#include<stdio.h>

#include<conio.h>

#include<stdlib.h>

#include<math.h>

void inverse(float a[10][10],int n)

{

int i, j, k;

float b[10][10], r;

for(i = 0; i< n; i++)

{

for(j = 0; j < n; j++)

b[i][j] = 0.0;

b[i][i] = 1.0;

}

for(k = 0; k < n; k++)

for(i = 0; i < n; i++)

{

if(i == k)

continue;

r = a[i][k] / a[k][k];

for(j = 0; j < n; j++)

{

a[i][j] -=r * a[k][j];

b[i][j] -= r * b[k][j];

}

}

for(i = 0; i<n; i++)

for(j = 0; j<n; j++)

b[i][j] = b[i][j] / a[i][i];

printf("The inverse matrix is \n");

for(i = 0; i <n; i++)

{

for(j = 0; j < n; j++)

printf("%3f \t",b[i][j]);

printf("\n");

}

}

main()

{

int i, j, k, n;

float a[10][10];

clrscr();

printf("Enter the order of the matrix\n");

scanf("%d",&n);

printf("Enter the elements of matrix \n");

for(i = 0; i < n; i++)

for(j = 0; j < n; j++)

scanf("%f",&a[i][j]);

inverse(a,n);

getch();

return 0;

}

Output:

Run 1:

Enter the order of the matrix

2

Enter the elements of matrix

1 2 3 4

The inverse matrix is

-2.000000 1.000000

1.500000 -0.500000

Run 2:

Enter the order of the matrix

3

Enter the elements of matrix

1.0 2.0 0.0 2.0 3.0 0.5 1.0 1.0 1.0

The inverse matrix is

-5.000000 4.000000 -2.000000

3.000000 -2.000000 1.000000

2.000000 -2.000000 2.000000