Determinant Questions

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

Find the determinant of $$\begin{vmatrix} sinx & cosx \\ -cosx & sinx \end{vmatrix}$$.

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