anonymous 4 years ago Somebody help me calculate the determinant of a 4*4 matrix..

1. anonymous

What is the matrix?

2. anonymous

If the matrix is diagonal then the determinant is the product of its diagonal entries. If it is not diagonal you can simplify the matrix using elementary row operations (which can change the sign of the determinant) to a diagonal matrix. Alternatively you can directly compute it without any simplification, but it can be more tedious. There is a 4x4 example here: http://people.richland.edu/james/lecture/m116/matrices/determinant.html under "larger order determinants"

3. anonymous

To directly compute,multiply each entry in the first row against the determinant of the 3x3 matrix formed by eliminating the top row and the column containing your current entry.

4. anonymous

^ then alternatively add and subtract the determinants for the 3x3 matrices

5. anonymous

is there any other method that can be used since the above one..is a bit tedious and long when your doing a two hours paper.......

6. anonymous

Do you need to show your work ?

7. anonymous

yes its required you show your work...

8. anonymous

What is the matrix? It can't be that bad :)

9. anonymous

$\left[\begin{matrix}1 & 2 &3&4 \\ 2 & -1&2&1\\3&7&1&2\\1&3&2&1\end{matrix}\right]$..you do that for me i'll certainly do the rest..:)

10. anonymous

See attached. Hope that helps.

11. anonymous

cse thank-you was however wondering if you don't breakdown the 3*3 to show how you come up with the determinant again,,,

12. anonymous

Sure np. I was just being lazy when I typed that up and skipped the 3x3 part. See attached.

13. anonymous

The main idea is you keep breaking up the big matrix into smaller matrices that you can calculate the determinant for. It will possibly be more confusing if I write a really lengthy post on how to do this but look at the diagram I drew and check out the video below: http://www.youtube.com/watch?v=21LWuY8i6Hw

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