Find the determinant of A = $$\begin{bmatrix} 3 & -2 & 4 \\ 1 & 2 & 1 \\ 0 & 1 & -1 \end{bmatrix}$$.

Solution :

| A | = $$\begin{vmatrix} 3 & -2 & 4 \\ 1 & 2 & 1 \\ 0 & 1 & -1 \end{vmatrix}$$

By using 3×3 determinant formula,

$$\implies$$ | A | = $$3\begin{vmatrix} 2 & 1 \\ 1 & -1 \end{vmatrix}$$ – $$(-2)\begin{vmatrix} 1 & 1 \\ 0 & -1 \end{vmatrix}$$ + $$4\begin{vmatrix} 1 & 2 \\ 0 & 1 \end{vmatrix}$$

$$\implies$$ | A | = 3(-2 – 1) + 2(-1 – 0) + 4(1 – 0)

= -9 – 2 + 4 = -7