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

 May 14, 2022
 #1
avatar+9457 
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Directly use the following property of determinants:

 

Suppose A is a square matrix. Then \(\det A = \det(A^{\top})\), where \(A^\top\) is the transpose of A.

 May 14, 2022
 #2
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I tried 24 but thats not it

imbadatmath  May 14, 2022
 #3
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Let \(A = \begin{pmatrix}a&b&c\\d&e&f\\g&h&i\end{pmatrix}\), you are given \(\det(A)\) = -24, and you are to find \(\det(A^{\top})\)

 

Combine this with the formula I stated. Is this clearer to you now?

MaxWong  May 14, 2022

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