## Calcmathlete 2 years ago Evaluate: $$\left[\begin{matrix}1 & 2 &1 & 3 \\2&3&2&0\\3&1&0&1\\0&0&3&2\end{matrix}\right]$$

1. Calcmathlete

I got -102. Is it correct or did I get an arithmetic error somewhere?

2. Zekarias

I got -98

3. Calcmathlete

Hmm... Let me just double check everything here...

4. Calcmathlete

$3\left[\begin{matrix}1 & 2 &3\\ 2 & 3 &0\\3&1&1\end{matrix}\right] - 2\left[\begin{matrix}1 & 2 &1\\ 2 & 3 &2\\3&1&0\end{matrix}\right]$Did you end up doing this?

5. TuringTest

determinant?

6. Calcmathlete

I think so.

7. TuringTest

must be method of cofactors, eh?

8. Calcmathlete

Yup...

9. asnaseer

I get 72. But maybe I made a mistake. Might be worth looking at this to help: http://people.richland.edu/james/lecture/m116/matrices/determinant.html

10. TuringTest

I get 72 as well

11. asnaseer

Look down that web page at the section titled "Larger Order Determinants"

12. TuringTest

another source for ya http://tutorial.math.lamar.edu/Classes/LinAlg/MethodOfCofactors.aspx

13. Calcmathlete

Well, 72 is one of my answer choices... I did it again, but I got - 72? I think it's just an arithmetic error on my part. THanks guys!

14. asnaseer

yw :) - crosses fingers in the hope that he did make a mistake :)

15. asnaseer

*did NOT ...

16. Calcmathlete

Wait, one last thing, when I find the determinants of the 3 x 3, can I just use the diagonal method (I'm not sure of the name) or do I have to use minors?

17. asnaseer

as @TuringTest said, use the method of cofactors - see the links we gave you.

18. Calcmathlete

Ok, once again, thank you :)

19. TuringTest

the problem in what you did is that you forgot that all elements on the diagonals will give positive minors.

20. TuringTest

I phrased that poorly, not sure how to say it without giving away the answer

21. asnaseer

Also, determinants are usually written with straight lines on either side of the matrix elements - instead of the square brackets that you used.

22. Calcmathlete

Oh! I got it! And @asnaseer for some reason, I see them written both ways when doing school work?

23. asnaseer

Hmmm - ok, well I was taught that straight lines is what should be used. Maybe the notation differs from country to country?

24. Calcmathlete

Perhaps.

25. TuringTest

if it's left in brackets it should at least say $$\det$$ in front of it In the US we use what @asnaseer said

26. asnaseer

Here is an example of how we are taught in the UK: http://www.intmath.com/matrices-determinants/matrix-determinant-intro.php

27. asnaseer

Also, when working with algebra, if you have a matrix A, then we would write its determinant as either:$|A|$or:$det(A)$