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Given that \(\begin{vmatrix} a & b & c \\ d & e & f \\ g & h & i \end{vmatrix} = -24,\) find \(\begin{vmatrix} a & d & g \\ b & e & h \\ c & f & i \end{vmatrix}.\)
 

 Jun 14, 2020
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Notice that \(\begin{bmatrix} a&d&g\\b&e&h\\c&f&i \end{bmatrix} = \begin{bmatrix} a&b&c\\ d&e&f\\ g&h&i \end{bmatrix}^{\mathbf{T}}\)

 

So their determinants are the same.

 

\(\begin{vmatrix} a & d & g \\ b & e & h \\ c & f & i \end{vmatrix} = \begin{vmatrix} a&b&c\\d&e&f\\g&h&i\end{vmatrix} = -24\)

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 Jun 14, 2020

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