How to solve a Non-Square Matrix Equation?

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To solve the equation A = BxC with the given matrix dimensions, one must recognize it as an underdetermined system, where the number of unknowns exceeds the number of equations. Since matrix C is not square, its inverse cannot be calculated directly, complicating the isolation of B. In such cases, solutions may either be nonexistent or infinite. A common approach to find a solution is to use the 'minimum norm' method, which provides a feasible solution when one exists. This technique is particularly useful when dealing with large matrices and underdetermined systems.
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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...
 
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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).
 

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