Problem3:The curve, 
> ;
2 y = a x + b x + c
passes through the points (x1,y1), (x2,y2), (x3,y3). Show that the coefficients a,b, and c are a solution of the system of linear equations whose augmented matrix is, 
> ;
[ 2 ] [x1 x1 1 y1] [ ] [ 2 ] [x2 x2 1 y2] [ ] [ 2 ] [x3 x3 1 y3]

Each pt. (x,y) on the plane produces the equation of the curve. i.e., 
> Eq := (x,y) > a*x^2+b*x+c = y;
2 Eq := (x, y) > a x + b x + c = y
since the curve must pass through each of the given points we have 3 equations in the unknowns a,b and c given by, 
> Eq(x1,y1); Eq(x2,y2); Eq(x3,y3);
2 a x1 + b x1 + c = y1 2 a x2 + b x2 + c = y2 2 a x3 + b x3 + c = y3
hence, the augmented matrix is the one specified in the problem. 