# matrix inversion

```> Please consider some of the fundamentals of matrix algebra.  Two matricies
> may only be added IFF they are of the same dimensions. (this is the [A] -1
> [B] equation you listed)
>
> What you are trying to do is subtract a 3x1 matrix from a 3x3 matrix.  It
> cannot be done.
> I will note, that I receive the error message of "Dimension Mismatch",
> rather than "Singular Matrix"
>
> Now, in the defenition of an inverse matrix is a matrix B=[b], such that
> A*B=I (Where "I" is the identity matrix.)
>
> Consider the three rows of the Matrix A. row one :  [.2,3,4], row two
> :[0,0,1], and row three : [-2,3,0].  Some of elemetary row operations
> allowed on matricies are row multiplication by a non-zero scalar, addition
> of a scalar multiple of one row onto another, and row swapping..  (I'm
> going to assume that this is a refresher for you, rather than a full blown
> course. :-)  )
> Consider the following row operations 4*R2 + R3 - R1.  (R1 = row one,
> etc...)  What's the answer?  zero.  Clearly, you have a set of linearly
> dependant row vectors.  Therefore the matrix is of rank less than it's
> dimension, therefore it is not invertable.
>
> Here's a quick way to figure out if a matrix is invertable.  Take it's
> determinant.  If the answer is zero, it's a singular matrix.  Also, find
> the RREF.  If it has a row of zeros, again, it's non-invertable.
>
> xizar

Thanks for the info. I kinda goofed. [A]-1[B] was SUPPOSED to be
[A]<inverse>[B], I just got a little sloppy. Sorry for the
mis-communication...

As far as the explaination, I must admit that I don't really know that
them. Be that as it may, 4*R2 + R3 - R1 seemed pretty straight forward
- no problems there. However, I don't know what the determinant is, or
how to find it. Same thing with ref and reff. What do they stand for,
and what do they do? Also, just what are you doing when you invert a
matrix? To me these seem like simple questions, but I'm starting to
get the idea that my "simple questions" have rather complicated