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