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<math>det(A)\left(\begin{array}{cccc}a11&a12\\a21&a22\end{array}\right)</math></math><br>
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Revision as of 15:52, 7 December 2011

Determinants

 If A is a square matrix then the determinant function is denoted by det and det(A)

For an instance we have a 2 x 2 matrix denominated A, therefore:


                                                                                         det(A) = [a11 ,  a12 ; a21 , a22 ]

As we already defined the determinant function we can write some formulas. The formulas for any 2 x 2 and 3 x 3 matrix will be:

                     

                      The determinant function for a 2 x 2 matrix is:


                                                                                         det(A) = [a11 , a12 ; a21 , a22] $ det(A)=\left(\begin{array}{cccc}a11&a12\\a21&a22\end{array}\right) $

                                                                                                = a11 * a22 - a12 * a21 


                       

                      The determinant function for a 3 x 3 matrix is: 


                                                                             det(A) = [a11 , a12, a13 ; a21 , a22 , a23 ; a31 , a32 , a33]

                                 = (a11 * a22 * a33) + (a12 * a23 * a31) + (a13 * a21 * a32) - (a12 * a21 * a33) - (a11 * a23 * a32) - (a13 * a22 * a31) 

                                                                                                


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