Determinant Questions

Solution : | A | = \(\begin{vmatrix} 3 & -2 & 4 \\ 1 & 2 & 1 \\ 0 & 1 & -1 \end{vmatrix}\) By using 3×3 determinant formula, \(\implies\) | A | = \(3\begin{vmatrix} 2 & 1 \\ 1 & -1 \end{vmatrix}\) – \((-2)\begin{vmatrix} 1 & 1 \\ 0 & -1 \end{vmatrix}\) + […]

Solution : Let | A | = \(\begin{vmatrix} sinx & cosx \\ -cosx & sinx \end{vmatrix}\) By using 2×2 determinant formula, we obtain | A | = ( \(sin^2x\)) – (\(-cos^2x\)) = \(sin^2x\) + \(cos^2x\) = 1