Linear Equations Problem involving Matrices

I'm having a bit of difficulty getting my code to work. The problem I need it for is as follows:

In a Cartesian Coordinate system the equation of a a circle with its center at point (a,b) a radius r is:

(x-a)^2+(y-b)^2=r^2

Given three points, (-1, 3.2), (-8,4), and (-6.5, -9.3), determine the equation of the circle that passes through the points. Solve the problem by deriving a system of three linear equations (substitute the points into the equation and solve the system. (a) Use the user-defined function GaussPivot (provided below). (b) Solve the system of equations using MATLAB's left division operation.

For both part a and b I seem to be having trouble with my matrix dimensions, because I keep receiving this error: Attempted to access ab(3,3); index out of bounds because size(ab)=[3,2]. Also, it says that I have an error in this line of GaussPivot: x® = ab (R,C)/ab(R,R); I'm not completely sure what to do though.

Here is the GaussPivot code:

function x = GaussPivot(a,b)
% 
% The function solves a system of linear equations ax = b using the Gauss
% elimination method with pivoting.
% 
% Input variables:
% a  - The matrix of coefficients.
% b  - Right-hand-side column vector of constants.
% 
% Output variable:
% x  - A column vector with the solution.
%
%
%   ab - augmented matrix
ab = [a,b];
%   R - # of rows   C - # of columns in ab
[R, C] = size(ab);
%
for j = 1:R - 1
% Pivoting section starts
   if ab(j,j) == 0              % Check if the pivot element is identically zero
    for k = j + 1:R
         if ab (k,j) ~= 0        % if the off-diagonal terms are not equal to zero
             abTemp = ab(j,:);  % 
             ab(j,:) = ab(k,:);
             ab(k,:) = abTemp;
             break
         end
     end
   end
% Pivoting section ends
   for i = j + 1:R
       ab(i,j:C) = ab(i,j:C) - ab (i,j)/ab(j,j)*ab(j,j:C);
   end
end
x = zeros(R,1);
x(R) = ab (R,C)/ab(R,R);
for i = R - 1:-1:1
    x(i) = (ab(i,C) - ab(i,i + 1:R)*x(i + 1:R))/ab(i,i);
end

I then made a separate m-file for part a.

   % x and y coordinates
  x=[-1 -8 -6.5]
  y=[3.2 4 -9.3]
  % Matrices with the equations
  A=[-2*x(1)-2*y(1);-2*x(2)-2*y(2);-2*x(3)-2*y(3)];
  B=[-(x(1)^2+y(1)^2);-(x(2)^2+y(2)^2);-(x(3)^2+y(3)^2)];
  %Solve for unknowns
  C=GaussPivot(A,B)
  a=C(1)
  b=C(2)
  r=sqrt(C(1)^2+C(2)^2-C(3)^2)

This is where I get my errors. Any help is greatly appreciated. Thank you!

[Torsten]

As far as I can see, your matrix A is (3x1), but it has to be (3x3).

Best wishes

Torsten.

[Claire]

Thank you! That helped a lot!