# Determinant of 5x5 matrix

1. Oct 21, 2009

### mexion

1. The problem statement, all variables and given/known data
so my problem is to calculate the determinant of this matrix
$$\left[\begin{array}{ccccc} 1 & 2 & 3 & 3 & 5 \\ 3 & 2 & 1 & 2 & 2 \\ 1 & 2 & 3 & 4 & 5 \\ -1 & 0 & -8 & 1 & 2 \\ 7 & 2 & 1 & 3 & 2 \end{array}\right]$$

2. Relevant equations

3. The attempt at a solution
my calculation -> http://img29.imageshack.us/img29/1120/21102009124.th.jpg [Broken]
i know to use Laplace, but my teacher said me "at first you should reduce matrix to 3x3 or even 2x2 - it's easier to calculate the determinant"
but i don't understand this methode at all.
i've done this problem and my solution is -379 and i know it's wrong (correct is -224)
please help.

Last edited by a moderator: May 4, 2017
2. Oct 21, 2009

### Donaldos

The third line of your second determinant is incorrect.

3. Oct 21, 2009

### mexion

Last edited by a moderator: May 4, 2017
4. Oct 21, 2009

### Donaldos

Your last determinant should be

$$\left|\begin{array}{cc} -18 & 1\\ -50 &9\end{array}\right|$$

not

$$\left|\begin{array}{cc} -18 & 0\\ -50 &9\end{array}\right|$$

5. Oct 21, 2009

### mexion

yeah, my bad
but thanks now it's correct
thanks a lot :)

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