Question

Evaluate: \(\left[\begin{matrix}1 & 2 &1 & 3 \\2&3&2&0\\3&1&0&1\\0&0&3&2\end{matrix}\right]\)

Answer 1

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

Answer 2

I got -98

Answer 3

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

Answer 4

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

Answer 5

determinant?

Answer 6

I think so.

Answer 7

must be method of cofactors, eh?

Answer 8

Yup...

Answer 9

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

Answer 10

I get 72 as well

Answer 11

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

Answer 12

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

Answer 13

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!

Answer 14

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

Answer 15

*did NOT ...

Answer 16

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?

Answer 17

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

Answer 18

Ok, once again, thank you :)

Answer 19

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

Answer 20

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

Answer 21

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

Answer 22

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

Answer 23

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

Answer 24

Perhaps.

Answer 25

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

Answer 26

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

Answer 27

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