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5th Degree Polynomial Matrix

  1. Mar 23, 2008 #1
    1. The problem statement, all variables and given/known data
    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




    3. The attempt at a solution

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

    Any assistance would be obliged.
     
    Last edited: Mar 23, 2008
  2. jcsd
  3. Mar 23, 2008 #2

    symbolipoint

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    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?
     
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