# Non-linear system proof

1. Jul 5, 2012

### icesalmon

1. The problem statement, all variables and given/known data
The curve y = ax2 + bx + c passes through the points Q(x1,y1) R(x2,y2), S(x3,y3). Show that the coefficients a, b, and c are a solution of the system of linear equations whose augmented matrix is x12 + x1 + 1 = y1
x22 + x2 + 1 = y2 x32 + x3 + 1 = y3
2. Relevant equations

3. The attempt at a solution

I don't know where to start, I tried creating linear equations using the points Q, R, and S and the point slope formula. but it got messy. This is from Anton's 10th edition of Linear Algebra with applications pg. 10

2. Jul 6, 2012

### dikmikkel

To check if something is a solutions means:
substitute the solution in the system and check that the LHS equals the RHS.

3. Jul 6, 2012

### LCKurtz

What you have written isn't a matrix, so that isn't the form you are looking for.

You don't need the point slope form. Just write the three equations given by requiring the points $(x_1,y_1),\,(x_2,y_2),\, (x_3,y_3)$ satisfy the equation $ax^2+bx+c = y$ and think about these three equations in the three unknowns $a,b,c$. What do you get for their augmented matrix?

P.S. That system in $a,b,c$ will not be a non-linear system.