C++ Program to Find Basis and Dimension of a Matrix

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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.

  1. #include<conio.h>
  2. #include<iostream>
  3. #include<math.h>
  4.  
  5. using namespace std;
  6. double d = 0;
  7. double det(int n, double mat[10][10]);
  8. double det(int n, double mat[10][10])
  9. {
  10.     double submat[10][10];
  11.     if (n == 2)
  12.         return ((mat[0][0] * mat[1][1]) - (mat[1][0] * mat[0][1]));
  13.     else
  14.     {
  15.         for (int c = 0; c < n; c++)
  16.         {
  17.             int subi = 0; //submatrix's i value
  18.             for (int i = 1; i < n; i++)
  19.             {
  20.                 int subj = 0;
  21.                 for (int j = 0; j < n; j++)
  22.                 {
  23.                     if (j == c)
  24.                         continue;
  25.                     submat[subi][subj] = mat[i][j];
  26.                     subj++;
  27.                 }
  28.                 subi++;
  29.  
  30.             }
  31.             d = d + (pow(-1, c) * mat[0][c] * det(n - 1, submat));
  32.         }
  33.     }
  34.     return d;
  35. }
  36. int main(int argc, char **argv)
  37. {
  38.  
  39.     cout << "Enter the number of vectors:\n";
  40.     int n;
  41.     cin >> n;
  42.     double mat[10][10];
  43.     cout << "Enter the vectors one by one:\n";
  44.     for (int i = 0; i < n; i++)
  45.     {
  46.         for (int j = 0; j < n; j++)
  47.         {
  48.             cin >> mat[j][i];
  49.         }
  50.     }
  51.     d = det(n, mat);
  52.     if (d != 0)
  53.         cout << "The vectors forms the basis of R" << n
  54.                 << " as the determinant is non-zero";
  55.     else
  56.         cout << "The vectors doesn't form the basis of R" << n
  57.                 << " as the determinant is zero";
  58.  
  59. }

Output:

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$ g++ BasisAndDimension.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
 
Enter the number of vectors:
4
Enter the vectors one by one:
2 3 5 8
1 6 2 9
3 4 2 7 
2 5 3 9
The vectors forms the basis of R4 as the determinant is non-zero

Sanfoundry Global Education & Learning Series – 1000 C++ Programs.

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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter