day06.sagews

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

[ 1 -1 -5 0] [-1 0 3 0] [ 0 2 4 0]

A.rref()

[ 1 0 -3 0] [ 0 1 2 0] [ 0 0 0 0]

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'))

3D rendering not yet implemented

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()

3D rendering not yet implemented

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

[ 1 -1 0] [-1 0 1] [ 0 2 1]

B.rref()

[1 0 0] [0 1 0] [0 0 1]

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

3D rendering not yet implemented