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Description of an Augmented Matrix

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Question: Suppose you have three points (x_1, y_1), (x_2, y_2), (x_3, y_3), and you wish to find a quadratic polynomial, y = a + bx + cx^2), whose graph goes through these points. When solving the resulting system of three equations in the three unknowns a, b, c, suppose the system turns out to be inconsistent. What must be true about the three points for this to occur? Give an example of three such points, write the corresponding augmented matrix, and reduce the matrix to echelon form.

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Solution Summary

This solution is enclosed within an attached Word document and shows how to reiterate the augmented matrix concept, in a clear and concise manner. All calculations, along with reasoning, are provided.

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The resulting equations are given by
So, the augmented matrix is
Applying the row operations , we get .
This is equivalent to
Further simplification leads to
The ...

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