Assuming y is a nonzero real number, I need to find the determinant of this matrix:
$$ \left[ \begin{array}{cc} 1 & y & y^2 \\ y & y^2 & y^3 \\ y^2 & y^3 & y^4 \end{array} \right] $$
Can anyone help me get started? I know the answer is 0 from using Mathematica. Thanks
Edit
If I pulled out y from a row and had
$$y*D \left[ \begin{array}{cc} 1 & y & y^2 \\ 1 & y & y^2 \\ y^2 & y^3 & y^4 \end{array} \right] $$
and $$ \left[ \begin{array}{cc} 1 & y & y^2 \\ 1 & y & y^2 \\ y^2 & y^3 & y^4 \end{array} \right] = 0$$
therefore,
$$ \left[ \begin{array}{cc} 1 & y & y^2 \\ y & y^2 & y^3 \\ y^2 & y^3 & y^4 \end{array} \right] = 0$$
is this correct?
Hint: Pick two rows (or two columns). Are they linearly independent?