ALPHA DIVISION

Question 117

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Question

For the

3\times 3

matrix

\begin{pmatrix}A&B&C\\D&E&F\\G&H&I\end{pmatrix}

, Jack says the determinant equals AEI+BFG+CDH-(CEG+BDI+AFH). Jim says the determinant equals

A\begin{vmatrix}E&F\\H&I\end{vmatrix}-B\begin{vmatrix}D&F\\G&I\end{vmatrix}+C\begin{vmatrix}D&E\\G&H\end{vmatrix}

. Who is correct?

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Question

For the

3\times 3

matrix

\begin{pmatrix}A&B&C\\D&E&F\\G&H&I\end{pmatrix}

, Jack says the determinant equals AEI+BFG+CDH-(CEG+BDI+AFH). Jim says the determinant equals

A\begin{vmatrix}E&F\\H&I\end{vmatrix}-B\begin{vmatrix}D&F\\G&I\end{vmatrix}+C\begin{vmatrix}D&E\\G&H\end{vmatrix}

. Who is correct?