with(linalg):
A := matrix(5,5);
num := rand(-5..5); # random numbers between -5 and 5
for i in {2,4,5} do
    for j from 1 to 5 do
        A[i,j] := num(); # random entry
od: od:
# col 1 is lin dep
for j from 1 to 5 do
    A[1,j] := 2*A[2,j]-3*A[4,j]+A[5,j];
od:
# col 3 is lin dep
for j from 1 to 5 do   
    A[3,j] := A[2,j]+2*A[4,j]-2*A[5,j];
od:
print(A);
# a single solution
x := matrix(5,1,[1,2,3,-2,1]);
# right hand vector
b := evalm(A &* x);
linsolve(A,b);