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- Thread starter Spunky_Dunky
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Spunky_Dunky said:

you break it up into three 2x2 determinents!

http://mathworld.wolfram.com/Determinant.html

look at the first line of eqt. 27

- #3

TD

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[tex]\begin{gathered}

A = \left( {\begin{array}{*{20}c}

{a_{11} } & {a_{12} } & {a_{13} } \\

{a_{21} } & {a_{22} } & {a_{23} } \\

{a_{31} } & {a_{32} } & {a_{33} } \\

\end{array} } \right) \Rightarrow \det \left( A \right) = \left| {\begin{array}{*{20}c}

{a_{11} } & {a_{12} } & {a_{13} } \\

{a_{21} } & {a_{22} } & {a_{23} } \\

{a_{31} } & {a_{32} } & {a_{33} } \\

\end{array} } \right| \hfill \\ \\

= a_{1,1}\cdot{a}_{2,2}\cdot{a}_{3,3} + a_{1,3}\cdot{a}_{3,2}\cdot{a}_{2,1} + a_{1,2}\cdot{a}_{2,3}\cdot{a}_{3,1} -

a_{1,3}\cdot{a}_{2,2}\cdot{a}_{3,1} - a_{1,1}\cdot{a}_{2,3}\cdot{a}_{3,2} - a_{1,2}\cdot{a}_{2,1}\cdot{a}_{3,3} \hfill \\

\end{gathered} [/tex]

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thanks very much

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TD said:

[tex]\begin{gathered}

A = \left( {\begin{array}{*{20}c}

{a_{11} } & {a_{12} } & {a_{13} } \\

{a_{21} } & {a_{22} } & {a_{23} } \\

{a_{31} } & {a_{32} } & {a_{33} } \\

\end{array} } \right) \Rightarrow \det \left( A \right) = \left| {\begin{array}{*{20}c}

{a_{11} } & {a_{12} } & {a_{13} } \\

{a_{21} } & {a_{22} } & {a_{23} } \\

{a_{31} } & {a_{32} } & {a_{33} } \\

\end{array} } \right| \hfill \\ \\

= a_{1,1}\cdot{a}_{2,2}\cdot{a}_{3,3} + a_{1,3}\cdot{a}_{3,2}\cdot{a}_{2,1} + a_{1,2}\cdot{a}_{2,3}\cdot{a}_{3,1} -

a_{1,3}\cdot{a}_{2,2}\cdot{a}_{3,1} - a_{1,1}\cdot{a}_{2,3}\cdot{a}_{3,2} - a_{1,2}\cdot{a}_{2,1}\cdot{a}_{3,3} \hfill \\

\end{gathered} [/tex]

oh, right. that crap.

:tongue:

my calc III prof went over that, mainly as a curiosity. i've used expansion by minors exclusively.

whatever's easiest to you!

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TD

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- #7

HallsofIvy

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TD said:

that's a really good idea. would have really come in handy when i was in 11th grade. (we had the occasional 4x4 determinant! :yuck: )

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