Difference between revisions of "Determinants MA265F11Walther" - Rhea

Revision as of 14:55, 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:

$det(A)=\left(\begin{array}{cccc}a11&a12\\a21&a22\end{array}\right)$ = (a₁₁ * a₂₂₎ - (a₁₂ * a₂₁)

The determinant function for a 3 x 3 matrix is:

$det(A)=\left(\begin{array}{cccc}a11&a12&a13\\a21&a22&a23\\a31&a32&a33\end{array}\right)$ </math>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)

@@ Line 17: / Line 17: @@
 <br>
-&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;'''det(A)''' = [a<sub>11</sub> , a<sub>12</sub>&nbsp;; a<sub>21</sub> , a<sub>22</sub>]&nbsp;<math>det(A)=\left(\begin{array}{cccc}a11&a12\\a21&a22\end{array}\right)</math>
+&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;<math>det(A)=\left(\begin{array}{cccc}a11&a12\\a21&a22\end{array}\right)</math>&nbsp;= ('''a<sub>11</sub> * a<sub>22)</sub> - (a<sub>12</sub> * a'''<sub>'''21'''</sub><sub>'''&nbsp;'''</sub>) &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
-&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = '''a<sub>11</sub> * a<sub>22</sub> - a<sub>12</sub> * a'''<sub>'''21&nbsp;'''</sub>
+&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
-<br>
-&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; The determinant function for a 3 x 3 matrix is:&nbsp;
@@ Line 29: / Line 25: @@
 <br>
-&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; det(A) = [a<sub>11</sub> , a<sub>12</sub>, a<sub>13</sub>&nbsp;; a<sub>21</sub> , a<sub>22</sub> , a<sub>23</sub>&nbsp;; a<sub>31</sub> , a<sub>32</sub> , a<sub>33</sub>]
+&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; <math>det(A)=\left(\begin{array}{cccc}a11&a12&a13\\a21&a22&a23\\a31&a32&a33\end{array}\right)</math></math>det(A) = [a<sub>11</sub> , a<sub>12</sub>, a<sub>13</sub>&nbsp;; a<sub>21</sub> , a<sub>22</sub> , a<sub>23</sub>&nbsp;; a<sub>31</sub> , a<sub>32</sub> , a<sub>33</sub>]
 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;= '''(a<sub>11</sub> * a<sub>22</sub> * a<sub>33</sub>) + (a<sub>12</sub> * a<sub>23</sub> * a<sub>31</sub>) + (a<sub>13</sub> * a<sub>21</sub> * a<sub>32</sub>) - (a<sub>12</sub> * a<sub>21</sub> * a<sub>33</sub>) - (a<sub>11</sub> * a<sub>23</sub> * a<sub>32</sub>) - (a<sub>13</sub> * a<sub>22</sub> * a<sub>31</sub>)&nbsp;'''

Difference between revisions of "Determinants MA265F11Walther" - Rhea

Revision as of 14:55, 7 December 2011

Determinants

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