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could someone please explain simply how to get the determinate of a 3 * 3 matrix I'm relly stuck I've looked through my textbooks but it only has examples of how to do it useing a grapgics calculator thanks
Spunky_Dunky said:could someone please explain simply how to get the determinate of a 3 * 3 matrix I'm relly stuck I've looked through my textbooks but it only has examples of how to do it useing a grapgics calculator thanks
TD said:You could do that, or use some properties first to create 0's and then develop to a row or column. There's also a direct way, but it's a bit 'long':
[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]
TD said:I usually expand by minors too, but not before I simplified it first using elementary operations. Having to expand it 'in full' is long too hehe