Solve the following equation for x
| x a x b |
| b x a x | = 0
| x b x a |
| a x b x |
(Determinant equals zero). I'm not sure how to do this and any help would be appreciated!
Do you know how to evaluate a 4x4 determinant?
$\displaystyle \displaystyle \begin{align*} \left|\begin{matrix} x & a & x & b \\ b & x & a & x \\ x & b & x & a \\ a & x & b & x \end{matrix}\right| &= x \left|\begin{matrix} x & a & x \\ b & x & a \\ x & b & x\end{matrix}\right| - a\left| \begin{matrix} b & a & x \\ x & x & a \\ a & b & x \end{matrix}\right| + x\left|\begin{matrix} b & x & x \\ x & b & a \\ a & x & x \end{matrix}\right| - b\left|\begin{matrix} b & x & a \\ x & b & x \\ a & x & b \end{matrix}\right| \end{align*}$
Can you evaluate each of these 3 x 3 determinants?