3101.sagews

print "Coefficient matrix at height 1"
M2 = matrix([
[1,-1,0,0,0],
[0,1,-1,0,0],
[0,0,-1,0,0],
[0,0,1,-1,0],
[0,0,0,1,-1],
]);
print M2
print "determinant =", M2.det();

print "Coefficient matrix at height 2"
M2 = matrix([
[1,-1,0,0,0],
[0,-1,-1,0,0],
[0,0,1,-1,0],
[0,1,0,-1,0],
[0,0,0,1,-1]
]);
print M2
print "determinant =", M2.det();

print "Coefficient matrix at height 3"
M2 = matrix([ 
[-1,-1,0 , 0,0 ], 
[0 , 1,-1,-1,0 ],
[0 , 0, 1, 0,-1],
[1 , 0, 0,-1, 0], 
[0 , 0, 0, 1,-1]
]);
print M2
print "determinant =", M2.det();


print "Coefficient matrix at height 4"
M2 = matrix([
[1,-1,-1,0],
[0,-1,0,0],
[0,0,1,-1],
[0,1,0,-1]
]);
print M2
print "determinant =", M2.det();

print "Coefficient matrix at height 5" 
M2 = matrix([
[-1,-1,0],
[0,1,0],
[1,0,-1],
]);
print M2
print "determinant =", M2.det();

print "Coefficient matrix at height 6" 
M2 = matrix([
[-1,0,0],
[0,-1,0],
[1,-1,-1]
]);
print M2
print "determinant =", M2.det();

print "Coefficient matrix at height 7" 
M2 = matrix([
[1,0],
[0,-1]
]);
print M2
print "determinant =", M2.det();

Coefficient matrix at height 1 [ 1 -1 0 0 0] [ 0 1 -1 0 0] [ 0 0 -1 0 0] [ 0 0 1 -1 0] [ 0 0 0 1 -1] determinant = -1 Coefficient matrix at height 2 [ 1 -1 0 0 0] [ 0 -1 -1 0 0] [ 0 0 1 -1 0] [ 0 1 0 -1 0] [ 0 0 0 1 -1] determinant = -2 Coefficient matrix at height 3 [-1 -1 0 0 0] [ 0 1 -1 -1 0] [ 0 0 1 0 -1] [ 1 0 0 -1 0] [ 0 0 0 1 -1] determinant = -3 Coefficient matrix at height 4 [ 1 -1 -1 0] [ 0 -1 0 0] [ 0 0 1 -1] [ 0 1 0 -1] determinant = 1 Coefficient matrix at height 5 [-1 -1 0] [ 0 1 0] [ 1 0 -1] determinant = 1 Coefficient matrix at height 6 [-1 0 0] [ 0 -1 0] [ 1 -1 -1] determinant = -1 Coefficient matrix at height 7 [ 1 0] [ 0 -1] determinant = -1