## More Problems on Linear Systems and Matrices

The parabola will have the form
. The three points will be on the parabola if and only if

The existence of such a parabola translates into the consistency
of the above system. Consider the augmented matrix

Take
and
to get

Take
and
to get

Now take
to get

From here, we can conclude that the parabola does exist. To find
it, let us continue with the row elementary operations. Take
and
to get

Finally take

Hence

or .

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