Where would you store a large, fluctuating Matrix?

I have a large matrix (~450x450) that I need to invert and multiply.
I’m hoping matrix.rb will do the trick for me.

The interesting part is that in addition to the base 450x450, I need
to accept new rows/columns into the matrix based on user input. So
the base is:

xxxxx and I will need to add xxxxxy or remove the y, or add
both xxxxxyz
xxxxx
xxxxxy
xxxxxyz
xxxxx
xxxxxy xxxxxyz
xxxxx
xxxxxy xxxxxyz
xxxxx
xxxxxy xxxxxyz

00000y 00000yz

00000zz

My question is,
(1) Where should I store these matrices? (in a static ruby
array, or in Mysql?)
(2) What methods will I need to manipulate the storage format
into one that’s accessible by Matrix.rb? (see below).

Thanks for your interest!

Matrix.rb

Matrix.rows([[25, 93], [-1, 66]])
Creates a matrix where rows is an array of arrays, each of which is a
row to the matrix. If the optional argument copy is false, use the
given arrays as the internal structure of the matrix without copying.

Wow, the illustrations didn’t come out the way I had hoped. Maybe
this will work better:

The base matrix is something like:

xxx
xxx
xxx

I’ll have to add other columns and rows (often more than one)

xxxy
xxxy
xxxy
000y

and also be able to remove them.