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December 23rd, 2014, 03:26 AM   #1
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Hello, why is the determinant turns out different using two different methods ?

its a 3x3 matrix.
method 1 -is using downwards diagonals multipication and adding
and then subtract from that the upwards diagonals multipication and subtracting.

method 2 - using minor extension.
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December 23rd, 2014, 11:32 AM   #2
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Hello, d2idan!

Your diagonal method is incorrect.

$\left[\begin{array}{ccc|cc} 2&0&1 & 2&0 \\
\text{-}3&1&1 & \text{-}3 & 1 \\
2&\text{-}1&0 & 2&\text{-}1 \end{array}\right]$

$\quad =\;(2)(1)(0) + (0)(1)(2) + (1)(\text{-}3)(\text{-}1) - (1)(1)(2) - (2)(1)(\text{-}1) - (0)(3)(0)$

$\quad =\; 0 + 0 + 3 - 2 + 2 - 0$

$\quad =\;3$

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December 23rd, 2014, 12:01 PM   #3
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Quote:
Originally Posted by soroban View Post
Hello, d2idan!

Your diagonal method is incorrect.

$\left[\begin{array}{ccc|cc} 2&0&1 & 2&0 \\
\text{-}3&1&1 & \text{-}3 & 1 \\
2&\text{-}1&0 & 2&\text{-}1 \end{array}\right]$

$\quad =\;(2)(1)(0) + (0)(1)(2) + (1)(\text{-}3)(\text{-}1) - (1)(1)(2) - (2)(1)(\text{-}1) - (0)(3)(0)$

$\quad =\; 0 + 0 + 3 - 2 + 2 - 0$

$\quad =\;3$

thanks ! , yes i understood
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