How to solve a Non-Square Matrix Equation?

[puki]

Homework Statement

I have to solve an equation like this:

Matrix A: dimensions [7000, 1]
Matrix B: dimensions [7000,8]
Matrix C: dimensions [8,1]

Matrix B is unknown.

Homework Equations

A=BxC

The Attempt at a Solution

I can't calculate the inverse of Matrix C because it is not square, then I don't know how to isolate B...

 

[hotvette]

Welcome to PF!

You have what is referred to as an 'underdetermined system' where there are more unknowns (8 x 7000 = 56000) than there are equations (i.e. 7000). In this situation there are either no solutions or an infinite number of solutions. If you are being asked to find 'any' solution, one common (though arbitrary) method is to find what is called the 'minimum norm' solution (assuming solutions exist).