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Unenlightened · #1 November 3rd, 2009, 12:08 AM

This question seems to be so basic that I can't find it anywhere... My grasp of linear algebra is embarrassing, and I'm working to remedy that, but I need this to produce something fairly sharpish...

Basically what I need is
the Kernel of, say, and how one gets it
$\left( \begin{array}{cccc} -1 & 0 & 0 & 1 \\ 1 & -1 & 0 & 0 \\ -1 & 0 & 1 & 0 \\ 0 & 1 & 0 & -1 \\ 0 & 0 & -1 & 1 \\ 0 & -1 & 1 & 0 \end{array} \right)$

and the Image of
$\left( \begin{array}{cccccc} -1 & -1 & 0 & -1 & 0 & 0 \\ 1 & 0 & -1 & 0 & -1 & 0 \\ 0 & 1 & 1 & 0 & 0 & -1 \\ 0 & 0 & 0 & 1 & 1 & 1 \end{array} \right)$

I need it to calculate the homology, ie. using Ker i / Im j

Many thanks...