## Problem on computing the determinant of a 3x3 matrix

Compute the determinant of $$\begin{pmatrix}1 & -1& 1 \\ 1 & 1 & 1\\1 & 2 & 4 \end{pmatrix}$$
• ## Solution

Recall that
The determinant of $\begin{pmatrix}1 & -1& 1 \\ 1 & 1 & 1\\1 & 2 & 4 \end{pmatrix}$ is thus \begin{align} 1\cdot 1 \cdot 4 &+ (-1) \cdot 1 \cdot 1 + 1\cdot 1\cdot 2 \\ &- 1\cdot 1 \cdot 1 - (-1) \cdot 1 \cdot 4 - 1 \cdot 1 \cdot 2,\end{align}
which simplifies to $$\text{det } \begin{pmatrix}1 & -1& 1 \\ 1 & 1 & 1\\1 & 2 & 4 \end{pmatrix} = 6.$$