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I would like to define a function which produce matrices with variables. It will be something like the following.

def MatrixG(x,n,m):
    r=Matrix(n,m)
    for i in [0..n-1]:
        for j in [0..m-1]:
            r[i,j]=x[i,j]
    return r

Here x[i,j]'s are variables. How to write the above correctly in Sage? Thank you very much.

I would like to define a function which produce matrices with variables. It will be something like the following.

def MatrixG(x,n,m):
    r=Matrix(n,m)
    for i in [0..n-1]:
        for j in [0..m-1]:
            r[i,j]=x[i,j]
    return r

Here x[i,j]'s are variables. How to write the above correctly in Sage?

I also would like to have LU decomposition of some matrix like r1=MatrixG(3,3), r1 is a symbolic matrix.

Thank you very much.