Maple error - "illegal use of a formal parameter" - maple

Question

I'M TRYIN TO CREATE A PROGRAM USING MAPLE FOR GAUSSING ELIMINATION BUT I KEEP GETTING THIS ERROR
Gauss := proc (n::posint, A::matrix, c::Vector)
local a, i, k, j, p;
with(MTM):
n := linalg[rowdim](A);
if det(A) = 0 then print('matrice*doit*etre*caree')
else if det(A) <> 0
then a := `<|>`(A, c);
for k to n-1 do
for i from k+1 to n do
if a[i, i] = 0 then swaprow(a, k, i)
else p = a[i, k]/a[k, k];
for j from k+1 to n+1 do a[i, j] = a[i, j]-p*a[k, j]
end do;
end if;
end do;
end do;
else print('rien')
end if; end if; end proc;
Error, (in Gauss) illegal use of a formal parameter

Answer 1

restart;
Gauss := proc(A::Matrix, c::Vector)
local a, i, k, j, m, n, p;
n := linalg[rowdim](A);
m := linalg[coldim](A);
if m <> n then
print("matrice doit etre caree");
else
a := `<|>`(A, c);
for k to n-1 do
for i from k+1 to n do
if a[i, i] = 0 then
a := linalg[swaprow](a, k, i);
else
p := a[i, k]/a[k, k];
for j from k to n+1 do
a[i, j] := a[i, j]-p*a[k, j];
end do;
end if;
end do;
end do;
end if;
return a;
end proc:
c := Vector([2, 3, 4]);
A := Matrix(3, 3, [4, 1, 2, 3, 6, 5, 2, 1, 9]);
Gauss(A, c);
LinearAlgebra:-LUDecomposition(<A|c>, output=U);
There were quite a few mistakes, so let's hope I get most of them.
I didn't bother doing 7. You should do it.
You cannot use with inside a procedure.
Your code uses commands from thelinalg
package, not the MTM package.
Ideally you'd use Matrix&Vector&LinearAlgebra
(instead of your mix of matrix&Vector&linalg(.
Your procedure has n as one of its
parameters, but inside it you also try to
assign a value to n, the argument for which
you passed in as the number 3. That's where
your error message is coming from. You can't
do that.
Several of you lines have just = instead of
:= for assignments. The = does nothing.
The test against det(A)=0 is wrong is wrong
in several ways. I'll just say that it doesn't
actually test whether the A is square.
Compare the row & column dimensions if you
want to test that A is square.
You should be using LinearAlgebra
equivalents instead of the linalg commands
commands swaprow, coldim.
You forgot to have your procedure actually
return the Matrix a.
When your code calls swaprow is was not
actually updating a. It was just throwing
way the result.
It's a sin to not indent your code. It will
lead you to overlook mistakes.