# Re: matrix inversion

```x-no-archive : yes

Jody wrote:

> 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...

No problem.  That's what email and messages are all about.

> As far as the explaination, I must admit that I don't really know that
> much about matrics. Actually, I don't think I know anything about
> 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

What level math are you taking?  Or are you doing this for fun?  Personally, I
do enjoy toying with my calculator.  However, normally try to confine my
explorations to safe areas (i.e., where an instructor can bail me out of :-)

Anyway . . .

If I'm repeating myself here, sorry; I'm just trying to be as clear as
possible.

Mathematicians love two numbers: Zero and One.  Zero is nice because if you add
it to anything, you don't change anything.  If you multiply it by something, it
disappears.  One is One-derful, because if you multiply it by anything, you
(again) don't change a single thing.  There's also the good thing about the
reciprocals, and canceling stuff out, as well.

Well, consider.  What is the inverse of 2?  One half, correct?  This is true,
because if I take two, and multiply it by one half, I get one for an answer.

Well, taking the inverse of a matrix is the same idea.  If I have a matrix A,
and multiply it by B and get the Identity matrix for an answer, A is the
inverse
of B, and vice versa.What's that?  You don't know what an identity matrix is?
Consider a matrix "I" such that it's dimensions are square (i.e., an equal
number of rows and columns).  Now fill up the matrix with zeros.  Then, along
the main diagonal (the diagonal going from the top left corner to the bottom
right corner) stick in all ones.  In Matrix Algebra, this is equivelent of the
number one.  If there were no ones, then it would be a Zero matrix (just like
the number zero in conventional algebra).  However, the Zero matrix can be of
any dimension, not just square.

So, considering you know how to take the inverse on the calculator?  Well,
punch
the matrix in to the calculator (to learn how, refer to your manual).  Then
just
raise the matrix to the (-1) power.  Viola!  The inverse.

Other definitions:

REF   : Reduced echelon form
RREF : Row Reduced echelon form

These commands, as well as the Determinant can be found in the Matrix menu of

to explain these, I need you to actually have a rudimentary background in
Matrix