A = matrix([[1,-1,-5,0],[-1,0,3,0],[0,2,4,0]]); A

A.rref()

a = vector([1,-1,0]);
b = vector([-1,0,2]);
c = vector([-5,3,4]);
(plot(a,color='darkviolet')+plot(b,color='tomato')+plot(c,color='steelblue'))

aa = plot(3*a,color='darkviolet');
bb = plot(-2*b,start=3*a,color='tomato');
cc = plot(c,start=3*a-2*b,color='steelblue');
(aa+bb+cc).show()

d = vector([0,1,1]);
B = matrix([a,b,d]).transpose(); B

B.rref()

dd = plot(d,color='steelblue');
(plot(a,color='darkviolet')+plot(b,color='tomato')+plot(d,color='steelblue'))