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December 23rd, 2014, 03:26 AM  #1 
Newbie Joined: Dec 2014 From: Romania Posts: 5 Thanks: 0 Math Focus: linear algebra  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. 
December 23rd, 2014, 11:32 AM  #2 
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  Hello, d2idan! Your diagonal method is incorrect. $\left[\begin{array}{ccccc} 2&0&1 & 2&0 \\ \text{}3&1&1 & \text{}3 & 1 \\ 2&\text{}1&0 & 2&\text{}1 \end{array}\right]$ $\quad =\;(2)(1)(0) + (0)(1)(2) + (1)(\text{}3)(\text{}1)  (1)(1)(2)  (2)(1)(\text{}1)  (0)(3)(0)$ $\quad =\; 0 + 0 + 3  2 + 2  0$ $\quad =\;3$ 
December 23rd, 2014, 12:01 PM  #3  
Newbie Joined: Dec 2014 From: Romania Posts: 5 Thanks: 0 Math Focus: linear algebra  Quote:
 

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