The Pain of Inverting Matrices

For those who did not have the dubious pleasure of doing this in their first linear algebra class...it is painfully tedious to invert matrices (assuming that the matrix is invertible in the first place).

Basically, it involves performing many, many elementary row and column operations on the matrix until we get something that has a unit matrix in it (hard to explain without having actual matrices to point at, but anyway). After that, we get to multiply all the elementary matrices associated with the many, many elementary row and column operations to get two matrices, B (product of all elementary row matrices) and C (product of all elementary column matrices). CB = A-inverse.

It is even worse to express A in terms of elementary row and column matrices, because we have to invert each and every single one of the elementary matrices.

The most challenging part of it all is to make sure there are no arithmetical errors. Not a particularly fascinating occupation. And I am the worst number-cruncher I know, too. *Sigh*.

Remark: there may exist some neat tricks out there to make this process faster/less painful; I just don't know of them at the moment.

On a more cheerful note: two recrystallizations later, my CuSO₄ finally managed to crystallize into one large mass. It isn't perfect, but I am too lazy to dissolve it one more time. A picture will be uploaded...eventually (i.e. when I am not too lazy to dig out the cable necessary to upload my pictures).