How to Formulate a 6x6 Matrix for a 5th Degree Polynomial?

[Bob Ho]

Homework Statement

y=a0+a1x+a2x^2+a3x^3+a4x^4+a5x^5
(a0,a1...,a5, are fixed real numbers) passes through the points

(-2,21), (-1,7), (0,-10), (1,-8), (2,20), (3,9)

Question: Write down a 6x6 matrix A such that;


... .a0... ...21
. . .a1... ...7
. . .a2... ...-10
A . ..a3.. .= ...-8
. . .a4... ...20
. .a5... ...9

The Attempt at a Solution

I am unsure how to start this question. Do i substitute the points?

Any assistance would be obliged.

 

[symbolipoint]

You need only very slight linear algebra knowledge to begin.

Your coefficients are the unknowns, and the x and y values are given as the points.
You will have six equations and six unknowns. The column of y values should be the rightmost column in your matrix. Just elementary row operations (if this is not too simple-minded) could take much time. Might you be allowed to use a software?