How do you reduce a matrix with unknown components?

[Hertz]

Hi, I've been running into a problem lately where I have a system of equations that needs to be solved or I need to do some other sort of matrix algebra, but the components of the matrix that I am trying to perform row operations on have unknowns in them.

Specifically, I was working with a matrix who's components were all Kronecker Delta symbols. This was a problem because I didn't know which components were 1 and which components were 0, as it was not possible for them ALL to equal one or the other. Trying to put this matrix in RREF was troubling because I am not able to divide by the Kronecker Delta symbols as there is a large chance that they are zero. If I ignore this fact and solve traditionally anyways, I end up with rational answers that have delta symbols in the denominator, which is obviously not allowed.

So, I guess what I'm trying to ask is how do you reduce a matrix with unknown components? The traditional method of row operations does not work if there is a chance that these unknowns are equal to zero.

(I know you don't divide by rows in row operations. The problem is when you try to make the first non-zero component in a row equal to one, because you have to divide by its magnitude.)

 

[Bill Simpson]

Can you post the simplest, or at least a simple, example that demonstrates a real problem, the solution, why it is the solution and an explanation of the example? Maybe that would make it easier for someone to understand.

 

[AlephZero]

This was a problem because I didn't know which components were 1 and which components were 0, as it was not possible for them ALL to equal one or the other.

If you know the definition of the Kronecker delta symbol, you should be able to figure that out. You might need to write out some special cases for small matrices in full, to see what is going on.

Or, as Bill Simpson said, post an example.