Matrix Manipulation Homework: Inverting AB/BD for Epsilon & K

[lax1113]

Homework Statement

This is the equation for stresses and strains in a multilayered lamina. The actual purpose is irrelevant as I just am unsure what exactly the equation is saying (is it A * B * B^-1 * D^-1)
I am unfamiliar with this matrix syntax.

Homework Equations

Below is a link to an image of the actual equation that needs to be solved. Note that A, B, D are all 3 x 3 matrices, while epsilon, K, N and M are all 3x1 matrices.
http://ars.els-cdn.com/content/image/1-s2.0-S1359836802000021-si28.gif

The Attempt at a Solution

I honestly am completely unsure how to invert Matrix AB / BD as it is a matrix of 4 matrices, what function do we do to the matrix initially to get it to the form that will allow us to invert it, so that we can solve for epsilon and K (assuming we have N, M, A, B, D).

edit :::: Also, from my instructor, the matrix AB BD has dotted lines seperating each letter.
I also don't expect to do any hand manipulation as we are allowed to use TI89 on the test (so any kind of matrix manipulation that one can do with a calculator with a matrix function is fine)

 

[voko]

You do not really need to invert the matrix. You just substitute the matrix blocks for A, B, C, D and get a regular bigger-dimension matrix, which makes your problem a linear algebraic system, then you solve it (I guess your calculator should be able to do so).

You can also invert the resultant matrix, if you insist.

Finally, there a fancy way to invert a block matrix: http://en.wikipedia.org/wiki/Invertible_matrix#Blockwise_inversion

 

[lax1113]

Thank you very much. I wasn't entirely sure if that was what the matrix was claiming with the dotted lines between them (maybe thought this meant multiplication?) we really be we did much work with matrices other than an intro linear course.
Thanks again! Checked it and got the right answer.