I'm trying to fit a quadratic $a_0 + a_1x + a_2x^2$ by Polynomial Regression:

$$ \begin{pmatrix} n & \Sigma x_i & \Sigma x_i\\ \Sigma x_i & \Sigma x_i^2 & \Sigma x_i^3\\ \Sigma x_i^2 & \Sigma x_i^3 & \Sigma x_i^4\\ \end{pmatrix} \begin{pmatrix} a_0\\ a_1\\ a_2\\ \end{pmatrix}= \begin{pmatrix} \Sigma y_i\\ \Sigma x_iy_i\\ \Sigma x_i^2y_i\\ \end{pmatrix} $$ by Gaussian Elimination on the augmented matrix: $$ \left[ \begin{array}{ccc|c} n & \Sigma x_i & \Sigma x_i & \Sigma y_i\\ \Sigma x_i & \Sigma x_i^2 & \Sigma x_i^3 & \Sigma x_iy_i\\ \Sigma x_i^2 & \Sigma x_i^3 & \Sigma x_i^4 & \Sigma x_i^2y_i\\ \end{array} \right] $$

I'm not a matrix whizz, so how do I solve this using the same method when I know I want the y-intercept of the curve, $a0$, to be 0?