# Re: matrix inversion

```Jody wrote:

> I'm trying to invert martrix[A] for this program that I'm writing, but
> the calc keeps spitting up an error "ERR:SINGULAR MAT". Anyone know
> why? There was a small note mentioned in some of my paperwork for this
> program that says that the rows can't be multiples of each other.
> However, since I'm not familiar with what happens when a matrix is
> inverted, I don't know exactly what's wrong. Can someone tell my why I
> can't do [A]-1[B] with this:
> [A]
> [-2  3  4
>  0   0  1
>  -2  3  0]
> [B]
> [12
>  3
>  0]
> Thanks

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

```

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