## anonymous one year ago Find the value

1. anonymous

2. anonymous

@jim_thompson5910 how do i do this?

3. jim_thompson5910

|dw:1443914556285:dw|

4. jim_thompson5910

the vertical bars mean "determinant"

5. anonymous

So how would I find the value?

6. jim_thompson5910

step 1) copy the first 2 columns and write them to the right of the vertical bar |dw:1443914670674:dw|

7. anonymous

Ok and then what?

8. jim_thompson5910

step 2) group up the elements into subgroups by circling the elements along the diagonals like this (see circled) |dw:1443914609410:dw|

9. jim_thompson5910

step 3) multiply out the numbers in the sub groups |dw:1443914648908:dw|

10. jim_thompson5910

step 4) add up those products 6+0+(-3)=3 We'll use this number later. Let's call this "sum A"

11. jim_thompson5910

step 5) this is very similar to step 2, but now we're circling these diagonals (see below) |dw:1443914771771:dw|

12. jim_thompson5910

step 6) multiply out the numbers in the sub groups |dw:1443914811735:dw|

13. jim_thompson5910

step 7) add up those products 0+1+(-18)=-17 We'll use this number later. Let's call this "sum2"

14. jim_thompson5910

sorry sum B, but I guess it doesn't matter as long as you're consistent

15. jim_thompson5910

step 8 (final step) subtract the two sums sum A - sum B = 3 - (-17) = 3 + 17 = 20 so the determinant of this matrix is 20

16. anonymous

Value = determinant right? Same thing?

17. jim_thompson5910

hmm I messed up somewhere, let me think

18. jim_thompson5910

oh nvm, I just typed it into the calc wrong

19. anonymous

Ok so the final answer (value) is 20?

20. jim_thompson5910

$\Large \left|\begin{array}{ccc}1&2&-1\\3&-2&1\\0&1&-3\end{array}\right| = 20$ i.e., the determinant of this matrix is 20

21. anonymous

thx