I'll give you a hint: if you have a problem that can be formulated A*x = b, where A is a matrix and x,b are vectors, then you can solve for x using
x = A\b
EDIT: O. k., next hint: Ignore my symbol names, focus on which are vectors, e.g., x = [A_0; A_1; A_2; A_3; A_4].
EDIT 2: Here is how you do it:
b = [z_1; z_2; z_3; z_4; z_5]; % or b = [z_1 z_2 z_3 z_4 z_5]';
vx = [x_1; x_2; x_3; x_4; x_5];
vy = [y_1; y_2; y_3; y_4; y_5];
A = [ones(size(vx)) vx vx.^2 vy vy.^2];
x = A\b;
A_0 = x(1); A_1=x(2); %etc.
I strongly recommend that you work through some of the introductory material, for example Matrices and Arrays. MATLAB was originally built to handle stuff like this, and it is designed to make it easy.
