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anonymous
 one year ago
Find the value
anonymous
 one year ago
Find the value

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@jim_thompson5910 how do i do this?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2dw:1443914556285:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2the vertical bars mean "determinant"

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So how would I find the value?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2step 1) copy the first 2 columns and write them to the right of the vertical bar dw:1443914670674:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2step 2) group up the elements into subgroups by circling the elements along the diagonals like this (see circled) dw:1443914609410:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2step 3) multiply out the numbers in the sub groups dw:1443914648908:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2step 4) add up those products 6+0+(3)=3 We'll use this number later. Let's call this "sum A"

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2step 5) this is very similar to step 2, but now we're circling these diagonals (see below) dw:1443914771771:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2step 6) multiply out the numbers in the sub groups dw:1443914811735:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2step 7) add up those products 0+1+(18)=17 We'll use this number later. Let's call this "sum2"

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2sorry sum B, but I guess it doesn't matter as long as you're consistent

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2step 8 (final step) subtract the two sums sum A  sum B = 3  (17) = 3 + 17 = 20 so the determinant of this matrix is 20

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Value = determinant right? Same thing?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2hmm I messed up somewhere, let me think

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2oh nvm, I just typed it into the calc wrong

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok so the final answer (value) is 20?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2\[\Large \left\begin{array}{ccc}1&2&1\\3&2&1\\0&1&3\end{array}\right = 20\] i.e., the determinant of this matrix is 20
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