What is the determinant of this 5x5 matrix and how can it be calculated?

[mexion]

Homework Statement

so my problem is to calculate the determinant of this matrix
\left[\begin{array}{ccccc}<br /> 1 &amp; 2 &amp; 3 &amp; 3 &amp; 5 \\<br /> 3 &amp; 2 &amp; 1 &amp; 2 &amp; 2 \\<br /> 1 &amp; 2 &amp; 3 &amp; 4 &amp; 5 \\<br /> -1 &amp; 0 &amp; -8 &amp; 1 &amp; 2 \\<br /> 7 &amp; 2 &amp; 1 &amp; 3 &amp; 2<br /> \end{array}\right]

Homework Equations

The Attempt at a Solution

my calculation -> http://img29.imageshack.us/img29/1120/21102009124.th.jpg
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.

 

[Donaldos]

The third line of your second determinant is incorrect.

 

[mexion]

yeah my bad.
but I've done it again ... and again wrong :(
http://img41.imageshack.us/img41/7408/21102009125.th.jpg

 

[Donaldos]

Your last determinant should be

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

not

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

 

[mexion]

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