Calculating Determinants

An $\mathbf{n=2}$ Example


$\displaystyle M$ $\textstyle =$ $\displaystyle \left(
\begin{array}{cccc}
3 & -1 \\
5 & 7
\end{array}\right)$  
$\displaystyle \vert M\vert$ $\textstyle =$ $\displaystyle 3 \cdot 7 - (-1)\cdot 5 = 21 + 5$ (5)
  $\textstyle =$ $\displaystyle 26$ (6)

An $\mathbf{n=3}$ Example


$\displaystyle M$ $\textstyle =$ $\displaystyle \left(
\begin{array}{cccc}
4 & 2 & 5 \\
-1 & 6 & 7 \\
3 & 1 & 2
\end{array}\right)$  
$\displaystyle \vert M\vert$ $\textstyle =$ $\displaystyle 4
\left\vert
\begin{array}{cccc}
6 & 7 \\
1 & 2
\end{array}\righ...
...
\,+\, 5
\left\vert
\begin{array}{cccc}
-1 & 6 \\
3 & 1
\end{array}\right\vert$  
  $\textstyle =$ $\displaystyle 4 \, (6 \cdot 2 - 7 \cdot 1)
- 2 \, ((-1) \cdot 2 - 7 \cdot 3)
+ 5 \, ((-1) \cdot 1 - 6 \cdot 3)$  
  $\textstyle =$ $\displaystyle 20 + 46 - 95$  
  $\textstyle =$ $\displaystyle -29$ (7)



Copyright © 2002-2004, Lewis A. Riley Updated Mon Jan 19 13:29:10 2004

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