Matrix doing a cofactor expansion

**lin.13579** · Aug 31st 2009, 08:06 PM

Evaluate the determinant of the following matrix A =
$ \left|\begin{array}{ccccc}2 & 1 & -3 & -1 & 2 \\ 0 & -1 & 0 & 3 & 1 \\ 0 & 2 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 & 2 \\ 0 & 3 & 0 & 3 & 2 \end{array}\right| $

by doing a co-factor expansion.

Please expalin how to do it, thank you!
this is the exercise on my task

**eXist** · Aug 31st 2009, 09:10 PM

If you have:

$\begin{array}{lcr} \mbox a & b & c \\ \mbox d & e & f \\ \mbox g & h & i\end{array} $

The cofactor for $a$ is the determinant of:

$\begin{array}{lcr} \mbox e & f \\ \mbox h & i \end{array} $

The cofactor for $b$ is negative(-) of the determinant of:

$\begin{array}{lcr} \mbox d & f \\ \mbox g & i \end{array} $

The cofactor for $c$ is the determinant of:

$\begin{array}{lcr} \mbox d & e \\ \mbox g & h \end{array} $

**HallsofIvy** · Sep 1st 2009, 06:38 AM

Why are you being asked to do a "co-factor expansion" if you don't know what that is?

I would recommend starting your co-factor expansion using the first column. That way you just have 2 times $\left|\begin{array}{cccc}-1 & 0 & 3 & 1 \\ 2 & 0 & 0 & 1 \\ 0 & 1 & 0 & 2 \\ 3 & 0 & 3 & 2\end{array}\right|$ and expand that determinant on the second column. Do you see why?

**lin.13579** · Sep 2nd 2009, 04:10 PM

Originally Posted by HallsofIvy

Why are you being asked to do a "co-factor expansion" if you don't know what that is?

I would recommend starting your co-factor expansion using the first column. That way you just have 2 times $\left|\begin{array}{cccc}-1 & 0 & 3 & 1 \\ 2 & 0 & 0 & 1 \\ 0 & 1 & 0 & 2 \\ 3 & 0 & 3 & 2\end{array}\right|$ and expand that determinant on the second column. Do you see why?

I am sorry, I am not good on maths , can you explain more please !!!
I don't understand what is "just have 2 times" mean?
Is it mean 2 times every number 1 & 0 & 3 & 1 \\ 2 & 0 & 0 & 1 \\ 0 & 1 & 0 & 2 \\ 3 & 0 & 3 & 2 to evaluate matrix A?

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