Question

Evaluate the following determinate. Write your answer as a polynomial in x.

[ a-x, b, c ]
[ 1 , -x, 0 ]
[ 0, 1, -x ]

Answer 1

\[\det\left[\begin{matrix} a & b & c\\d & e & f \\ g & h & i\end{matrix}\right]=a \ \det\left[\begin{matrix} e & f \\ h & i\end{matrix}\right]-b \ \det\left[\begin{matrix} d & f \\ g & i\end{matrix}\right]+c \ \det\left[\begin{matrix} d & e \\ g & h\end{matrix}\right]\]

Answer 2

\[\det\left[\begin{matrix} a-x & b & c\\1 & -x & 0 \\ 0 & 1 & -x\end{matrix}\right]=(a-x) x^2-b(-x)+c\]?????