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I have just started teaching linear algebra to myself. I know nothing about linear algebra so if this question seems simple please bare with me.

What do I do to show that the coefficients, a,b, and c of y=ax^2+bx+c are a solution of the system of linear equations whose augmented matrix is

[tex] \begin{pmatrix}

x_1^{2} & x_1 & 1 & y_1 \\

x_2^{2} & x_2 & 1 & y_2 \\

x_3^{2} & x_3 & 1 &y_3 \end{pmatrix} [/tex]

Where the points (x1,y1), (x2,y2) and (x3,y3) are three seperate points on the curve y. As a matter of fact I am trying to envisage the three linear equations and how they are related to the curve y. Thanks. The title is not accurate.

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# Use an augmented matrix to prove

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