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- #1

So here is the matrix representation using x, y, z, and t as the diagonals from left to right and x being the first order, y second order, z third order, t fourth order:

[tex]\left[ \begin{array}{cccc}1 & -2 & 3 & 1 \\-2 & 4 & 1 & 2 \\3 & 1 & 5 & -3 \\1 & 2 & -3 & -1 \\\end{array} \right][/tex]

Row echelon:

[tex]\left[ \begin{array}{cccc}1 & -2 & 3 & 1 \\0 & 7 & -4 & -6 \\0 & 0 & 7 & 4 \\0 & 0 & 0 & \frac{174}{49} \\\end{array} \right][/tex]

NOTE: Rows 2 and 3 were switched during this process!! (It was unavoidable.)

Now, I'm not sure what to do with this matrix, as it's no longer the same matrix that represents the original quadratic.