Write a program in Python to solve the homogenous system Ax=0 and write the general solution in parametric vector form. Your program should accept as input the size of the matrix, i.e. the number of rows and the number of columns of A, and also the entries of A.

No pre-existing routines from Python libraries should be used.

Note- Take a m X n matrix as input and convert it into its reduced row echelon form without using libraries and then write the general solution in pragmetric form using the reduced row echelon matrix.

please also explain how the code works as I have spent 4 hours and still couldn't make it work. please don't use too complex python for the code.

Thanks.

These are some test cases.

34114112124311 SOLUTION : [,,,]+x3[.5,1.5,1.,1] 35123246156358032 PIVOT POSITION: [(,),(1,2),(2,4)] RREF : 1.02.0.03.33333333333333350.0 0.00.01.00.33333333333333330.0 0.00.0.0.01.0 SOLUTION: [,,,,]+x_1[2.,1,.,,.]+x_3[3.3333333333333335,,.3333333333333333,1,.]