(1) ∣1ωω2ωω21ω21ω∣=ω3+ω3+ω3−ω6−1−ω3=2ω3−ω6−1=2−1−1=0\begin{vmatrix} 1 & \omega & \omega^2 \\ \omega & \omega^2 & 1 \\ \omega^2 & 1 & \omega \end{vmatrix} = \omega^3 + \omega^3 + \omega^3 - \omega^6 - 1 - \omega^3 = 2\omega^3 - \omega^6 - 1 = 2 - 1 - 1 = 01ωω2ωω21ω21ω=ω3+ω3+ω3−ω6−1−ω3=2ω3−ω6−1=2−1−1=0 (2) ∣x−1001x−1001x−1001x∣=x∣x−101x−101x∣−∣−100xx−111x∣\begin{vmatrix} x & -1 & 0 & 0 \\ 1 & x & -1 & 0 \\ 0 & 1 & x & -1 \\ 0 & 0 & 1 & x \end{vmatrix} = x\begin{vmatrix} x & -1 & 0 \\ 1 & x & -1 \\ 0 & 1 & x \end{vmatrix} - \begin{vmatrix} -1 & 0 & 0 \\ x & x & -1 \\ 1 & 1 & x \end{vmatrix}x100−1x100−1x100−1x=xx10−1x10−1x−−1x10x10−1x =x(x3+x+x)−(−x2−1)=x4+2x2+x2+1=x4+3x2+1= x(x^3 + x + x) - (-x^2 - 1) = x^4 + 2x^2 + x^2 + 1 = x^4 + 3x^2 + 1=x(x3+x+x)−(−x2−1)=x4+2x2+x2+1=x4+3x2+1