Find the determinant of the matrix $A=\left(\begin{array}{ccc}2& -1& 3\\ 0& 5& -2\\ 4& 1& 0\end{array}\right)$.

Step-by-step solution

1. Compute the determinant using cofactor expansion along the first row.
2. $\det A=2\det \left(\begin{array}{cc}5& -2\\ 1& 0\end{array}\right)-(-1)\det \left(\begin{array}{cc}0& -2\\ 4& 0\end{array}\right)+3\det \left(\begin{array}{cc}0& 5\\ 4& 1\end{array}\right)$
3. Evaluate each 2$\times$ 2 determinant: $5\cdot 0-(-2)cdot1=2$, $0cdot0-(-2)cdot4=8$, $0cdot1-5cdot4=-20$.
4. Substitute back: $2\times 2-(-1)\times 8+3\times (-20)=4+8-60=-48$.

Concept tested: Determinant of a 3x3 matrix

Published 7 September 2026 · Last updated 16 September 2026 · How this solution was prepared and checked