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Non-linear system proof

  1. Jul 5, 2012 #1
    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. jcsd
  3. Jul 6, 2012 #2
    To check if something is a solutions means:
    substitute the solution in the system and check that the LHS equals the RHS.
     
  4. Jul 6, 2012 #3

    LCKurtz

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    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.
     
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