- #1
DryRun
Gold Member
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Homework Statement
Use the properties of the determinant of a matrix to show that[tex]\begin{vmatrix}1+x^2 & x & 1 \\ 1+y^2 & y & 1 \\ 1+z^2 & z & 1\end{vmatrix}=(x-y)(x-z)(y-z)[/tex]
Homework Equations
Properties of determinants. There's 10 of them, according to my notes.
The Attempt at a Solution
I used the property where the scalar multiple of -1 of the third column added to the first column gives:[tex]\begin{vmatrix}x^2 & x & 1 \\ y^2 & y & 1 \\ z^2 & z & 1\end{vmatrix}[/tex]
And then I'm stuck.