That is right, in your special case the result of 'V_prime_matrix[6][1] * d_prime_matrix[1][6]' es quivalent to the scalar product (http://en.wikipedia.org/wiki/Scalar_product) - so you can rewrite your code to just one loop:

```
int f_bar = 0;
for (int i = 0; i < 6; i++)
{
f_bar += V_prime_matrix[x][0] * d_prime_matrix[0][i];
cout << f_bar << endl;
}
```