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| − | '''det(A)''' = [a<sub>11</sub> , a<sub>12</sub> ; a<sub>21</sub> , a<sub>22</sub>] | + | '''det(A)''' = [a<sub>11</sub> , a<sub>12</sub> ; a<sub>21</sub> , a<sub>22</sub>] <math>det(A)=\left(\begin{array}{cccc}a11&a12\\a21&a22\end{array}\right)</math> |
| − | = '''a<sub>11</sub> * a<sub>22</sub> - a<sub>12</sub> * a'''<sub>'''21 '''</sub> | + | = '''a<sub>11</sub> * a<sub>22</sub> - a<sub>12</sub> * a'''<sub>'''21 '''</sub> |
| − | + | <br> | |
| | ||
Revision as of 14:52, 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)
