If $x = \frac{a}{b-c}$, $y = \frac{b}{c - a}$, $z = \frac{c}{a - b}$ then what is the value of the following?

$\begin{vmatrix} 1 & -x & x\\ 1 & 1 & -y\\ 1 & z & 1 \end{vmatrix}$

The element in the i^th row and the j^th column of a determinant of third order is equal to 2(i + j). What is the value of the determinant?

With the numbers 2, 4, 6, 8, all the possible determinants with these four different elements are constructed. What is the sum of the values of all such determinants?

If the determinant $\left| {\begin{array}{*{20}{c}} x&1&3\\ 0&0&1\\ 1&x&4 \end{array}} \right| = 0$ then what is x equal to?