Compute the determinant of the matrix \begin{bmatrix}5 & -2\\ 3 & 4\end{bmatrix}.

Step-by-step solution

1. Compute $a=5$, $b=-2$, $c=3$, $d=4$.
2. Calculate $ad=5\times 4=20$.
3. Calculate $bc=(-2)\times 3=-6$.
4. Apply the formula $\det =ad-bc=20-(-6)=26$.
5. Thus the determinant is $26$.

Concept tested: Determinant of a 2x2 matrix

Published 16 October 2026 · How this solution was prepared and checked