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## anonymous one year ago ind the value of -6 -3 -5 5 7 -6 3 9 9

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1. jim_thompson5910

determinant of this matrix?

2. anonymous

-6

3. jim_thompson5910

can you post a screenshot of the full thing?

4. anonymous

I can't im sorry

5. jim_thompson5910

I'm confused what the full question is exactly

6. anonymous

finding the value

7. anonymous

it's only missing the brackets

8. jim_thompson5910

ok so this? $\Large \left|\begin{array}{ccc} -6 & -3 & -5\\ 5 & 7 & -6\\ 3 & 9 & 9\\ \end{array}\right|$

9. anonymous

yes

10. jim_thompson5910

ok so this is a determinant

11. jim_thompson5910

have you learned that term?

12. anonymous

I don't think i have

13. jim_thompson5910

|dw:1443314924015:dw|

14. jim_thompson5910

ok here is one method to do a determinant of a 3x3 matrix

15. jim_thompson5910

step 1) focus on the first two columns (circled) |dw:1443315068425:dw|

16. jim_thompson5910

copy those columns to the right of the matrix bar |dw:1443315093066:dw| keep the order the same

17. jim_thompson5910

we now have this extended matrix |dw:1443315131877:dw|

18. jim_thompson5910

step 2) draw diagonals that start at the top and face south east. I circled the terms eg: -6, 7 and 9 are the first group of terms |dw:1443315174379:dw|

19. jim_thompson5910

now multiply out the terms in each subgroup -6*7*9 = -378 -3*(-6)*3 = 54 -5*5*9 = -225

20. jim_thompson5910

then add up the products -378+54+(-225) = -549

21. jim_thompson5910

step 3) repeat the last step, but now we're going in the northeast direction |dw:1443315369919:dw|

22. jim_thompson5910

multiply out the subgroups 3*7*(-5) = -105 9*(-6)*(-6) = 324 9*5*(-3) = -135 add up the products -105+324+(-135) = 84

23. jim_thompson5910

the sum from step 2 was -549 the sum from step 3 was 84 subtract the sums like so -549-84 = -633 and that wraps up the problem

24. jim_thompson5910

It's a long process, but over time it should come easier with more practice

25. anonymous

thank you so much, it really seems a bit complicated but im starting to understand :3 @jim_thompson5910

26. jim_thompson5910

this page has a similar example http://www.sparknotes.com/math/algebra2/systemsofthreeequations/section3.rhtml

27. DanJS

Isn't that the same thing as doing the scalar triple product

28. DanJS

volume of parallellpipedd

29. DanJS

spaned by the three vectors

30. DanJS

(A x B) * C

31. jim_thompson5910

yes I think a 3x3 matrix determinant is involved somewhere in that

32. DanJS

vector cross product scalar triple product determinant |dw:1443320363438:dw|

33. DanJS

same thing, i just always remembered that way

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