Question

$\Delta = \begin{vmatrix} a & a+b & a+b+c \\ 3a & 4a+3b & 5a + 4b+3c \\ 6a & 9a+6b & 11a+9b+6c \end{vmatrix}$

Where a = 1, b = $\omega$, c = $\omega^2$, then $\Delta$ is equal

Answer 1

-1

Answer 2

1. Substitute $a=1$, $b=\omega$, $c=\omega^2$ and use $1+\omega+\omega^2=0$.
2. Perform row operations: $R_2-3R_1$ and $R_3-6R_1$.
3. Expand along the first column.
4. Simplify using $\omega+\omega^2=-1$ to get $\Delta = -1$.