m.ipynb

Kernel: SageMath (Development)

a1 = vector([1,2,3,4])
a2 = vector([1,0,1,0])
a3 = vector([-1,2,-1,0])
a4 = a1+2*a2+a3

A = matrix([a1,a2,a3,a4])

A

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

A.rref()

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

At = A.transpose()

At.rref()

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

3*a1+a2-a3

(5, 4, 11, 12)

2*a1+vector([1,1,1,1])

(3, 5, 7, 9)

-2*a1+a2

(-1, -4, -5, -8)

a1+a2

(2, 2, 4, 4)

-a1+a2

(0, -2, -2, -4)

B = matrix([a1,a2,a4,a3])

Bt = B.transpose()

Bt.rref()

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