[Question] Solving matrices of Stiffness Method

hi every one
i have problem in vb.net, solving a matrices-equation with the following scheme:

|-    -|    |-            -|   |-   -|
|  Q1  |    |  3  1  0  9  |   |  0  |
|  Q2  |    |  3  3  0  9  |   |  0  |
|  3   | =  |  4  0  0  7  | x |  D1 |
|  Q3  |    |  6  9  1  2  |   |  0  |
|-    -|    |-            -|   |-   -|

Is there any library for solving such equation?
if not, I need to answer this question:
* how could I manage to register variables Q1, Q2 ... etc in order to find their values?


I faced this problem while coding a library for structural analysis of beams by stiffness method