Finding parabola coefficients with a 3×3 matrix

[Hyperreality]

I'm having problems solving this particular question
Using matrix calculation to find a general solution for a parabola that passes through points (x1,y1), (x2, y2), (x3, y3).

First I setted my equations

ax1^2+bx2+c=y1

ax2^2+bx2+c=y2

ax3^2+bx2+c=y3

But I've no idea on how I should set up the augmented matrix. I presume the general solution is referring to the solving the constants a, b and c.

Any hints and suggestions is appreciated.

 

[arildno]

First of all, your equations are incorrect.
In the first equation, the term "bx2" should read "bx1", while in your third equation the term "bx2" should read "bx3" (I assume these were typos..)

Look at the the left-hand side of your equations.
How can you rewrite this side as a matrix-vector product, where you know the entries in the matrix, while the vector is the unknown?

 

[M98Ranger]

Hi there,

Solving a system of equations involving a parabola can be tricky, but using matrix calculations can make it much simpler. Here are some steps you can follow to find the general solution for a three-point parabola:

1. Set up your equations: As you have already done, start by setting up your equations using the three points given. This will give you three equations with three unknowns (a, b, and c).

2. Write the equations in matrix form: To solve the system of equations using matrices, we need to write them in the form of AX = B, where A is the coefficient matrix, X is the unknowns matrix, and B is the constant matrix. In this case, A will be a 3x3 matrix, X will be a 3x1 matrix, and B will be a 3x1 matrix.

3. Construct the augmented matrix: The augmented matrix is formed by combining the coefficient matrix and the constant matrix, separated by a vertical line. In this case, it will be a 3x4 matrix.

4. Use matrix operations to solve for X: Now that we have our augmented matrix, we can use matrix operations (such as row operations) to solve for X. Once you have the values for a, b, and c, you have found the general solution for the parabola.

I hope this helps! If you need more guidance, you can also try looking up examples of solving systems of equations using matrices. Good luck!