C Program to Find Basis and Dimension of a Matrix

This is a C Program to find the basis and dimension of the given matrix.

Here is source code of the C Program to Find Basis and Dimension of a Matrix. The C program is successfully compiled and run on a Linux system. The program output is also shown below.

```
#include<stdio.h>
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```
 
```
```
int main() {
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```
```
    int a[3][3], i, j;
```
```
 
```
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    long determinant;
```

    printf("Enter the 9 elements of matrix: ");

```
    for (i = 0; i < 3; i++)
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        for (j = 0; j < 3; j++)
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```
            scanf("%d", &a[i][j]);
```
```
 
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    printf("\nThe matrix is\n");
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    for (i = 0; i < 3; i++) {
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        printf("\n");
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        for (j = 0; j < 3; j++)
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            printf("%d\t", a[i][j]);
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    }
```
```
 
```

    determinant = a[0][0] * ((a[1][1] * a[2][2]) - (a[2][1] * a[1][2]))

            - a[0][1] * (a[1][0] * a[2][2] - a[2][0] * a[1][2]) + a[0][2]

            * (a[1][0] * a[2][1] - a[2][0] * a[1][1]);

```
 
```
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    if (determinant != 0)
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        printf("The vectors forms the basis of R %d as the determinant is non-zero", 3);

```
    else
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        printf("The vectors doesn't form the basis of R %d as the determinant is zero", 3);

```
 
```
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    return 0;
```
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}
```

Output:

$ gcc BasisDimension.cpp
$ ./a.out
 
Enter the number of vectors:
3
Enter the vectors one by one:
1 2 3
2 3 4
3 4 5
The vectors doesn't form the basis of R3 as the determinant is zero

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