Can you not just create the arrays manually?
int[] X = new int[] {x1.Value,x2.Value,x3.Value,x4.Value,x5.Value,x6.Value };
int[,] A = new int{ {a11.Value, a12.Value, a13.Value, a14.Value, a15.Value, a16.Value },
{a21.Value, a22.Value, a23.Value, a24.Value, a25.Value, a26.Value },
{a31.Value, a32.Value, a33.Value, a34.Value, a35.Value, a36.Value },
{a41.Value, a42.Value, a43.Value, a44.Value, a45.Value, a46.Value },
{a51.Value, a52.Value, a53.Value, a54.Value, a55.Value, a56.Value },
{a61.Value, a62.Value, a63.Value, a64.Value, a65.Value, a66.Value } };
Though it doesn't implement any neat tricks, it is incredibly easy, and quick. And because the amount of text boxes are unlikely to change once you start using it, there should be no problem hard coding it like this.
Also, you should use a square array, [,] rather than a jagged array, [][] because a jagged array can have different lengths on each row, which is undesirable in a matrix, and declaring it as square will be clearer.