Here's the question you clicked on:
Calcmathlete
Evaluate: \(\left[\begin{matrix}1 & 2 &1 & 3 \\2&3&2&0\\3&1&0&1\\0&0&3&2\end{matrix}\right]\)
I got -102. Is it correct or did I get an arithmetic error somewhere?
Hmm... Let me just double check everything here...
\[3\left[\begin{matrix}1 & 2 &3\\ 2 & 3 &0\\3&1&1\end{matrix}\right] - 2\left[\begin{matrix}1 & 2 &1\\ 2 & 3 &2\\3&1&0\end{matrix}\right]\]Did you end up doing this?
must be method of cofactors, eh?
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
Look down that web page at the section titled "Larger Order Determinants"
another source for ya http://tutorial.math.lamar.edu/Classes/LinAlg/MethodOfCofactors.aspx
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!
yw :) - crosses fingers in the hope that he did make a mistake :)
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?
as @TuringTest said, use the method of cofactors - see the links we gave you.
Ok, once again, thank you :)
the problem in what you did is that you forgot that all elements on the diagonals will give positive minors.
I phrased that poorly, not sure how to say it without giving away the answer
Also, determinants are usually written with straight lines on either side of the matrix elements - instead of the square brackets that you used.
Oh! I got it! And @asnaseer for some reason, I see them written both ways when doing school work?
Hmmm - ok, well I was taught that straight lines is what should be used. Maybe the notation differs from country to country?
if it's left in brackets it should at least say \(\det\) in front of it In the US we use what @asnaseer said
Here is an example of how we are taught in the UK: http://www.intmath.com/matrices-determinants/matrix-determinant-intro.php
Also, when working with algebra, if you have a matrix A, then we would write its determinant as either:\[|A|\]or:\[det(A)\]