Write a C program$($s$)$ that uses the Gauss$-$Jordan, Gauss$-$Seidel, and Jacobi methods to solve the following set of linear equations:

$Ax=b$

$12x_1+2x_2-2x_3+1x_4=-3$

$2x_1-4x_2+4x_3+15x_4=3$

$2x_1+18x_2+5x_3+5x_4=5$

$-2x_1+0x_2+12x_3-4x_4=-4$

Print the values of $x$ produced by the three methods. Also, print the number of iterations required for convergence for the Gauss$-$Seidel and Jacobi methods.

For the Gauss$-$Seidel and Jacobi methods, specify a reasonable convergence tolerance and the maximum number of iterations. Recall that there are certain conditions that must be met for these methods to be effective. You may need to modify this system before the algorithms begin.