Exercise · ZW-COFACTOR-LAPLACE-EXPANSION-001 · ★☆☆ Basic
For \(A=\begin{pmatrix}1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 10\end{pmatrix}\), compute the cofactor \(C_{12}\).
Choose one option.
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- B. \(2\)
Explanation
The minor is \(M_{12}=\det\begin{pmatrix}4&6\\7&10\end{pmatrix}=40-42=-2\) and the sign is \((-1)^{1+2}=-1\), so \(C_{12}=2\).
Review the concept: Cofactor and Laplace expansion
The minor \(M\) of an entry is the determinant of the submatrix left after deleting its row and column; the cofactor \(C\) is that minor with an alternating sign.
\[C_{ij}=(-1)^{i+j}M_{ij}\]
More practice problems: cofactor and laplace expansion
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