Show that the equation Ax = B can be solved by Gaussian elimination with scaled partial...

Show that the equation Ax = B can be solved by Gaussian elimination with scaled partial pivoting in (n³/3) + mn² + O(n²) multiplications and divisions, where A, X, and B are matrices of order n × n, n × m, and n×m, respectively. Thus, if B is n×n, then the n×n solution matrix X can be found by Gaussian elimination with scaled partial pivoting in multiplications and divisions.

Hint: If X^{( j )} and B^{(j )} are the j th columns of X and B, respectively, then AX^{(j )} = B^{(j )}.