Question

find the value of each determinant.

$\left|\begin{array}{ccc}2& -4& 6\\ 1& 4& 0\\ -1& 2& -4\end{array}\right|$

Short answer

The determinant of the given matrix is$-4$.

Step-by-step solution

Step 1. Given

$\left|\begin{array}{ccc}2& -4& 6\\ 1& 4& 0\\ -1& 2& -4\end{array}\right|$

Step 2. Calculation

$$\begin{gathered} \left|\begin{array}{ccc}2& -4& 6\\ 1& 4& 0\\ -1& 2& -4\end{array}\right| \\ =2\left[\left(4\times -4\right)-\left(0\times 2\right)\right]-\left(-4\right)\left[\left(-4\right)\times 1-0\times \left(-1\right)\right]+6\left[2\times 1-4\times \left(-1\right)\right] \\ =-4 \end{gathered}$$