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]
|
|
SOLUTION:
| 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. |