2345.sagews

A = matrix(RR,[[120,158, 175, 204, 232, 260, 288, 316, 343, 371],[1,1,1,1,1,1,1,1,1,1]])
A = A.transpose()
b = vector(RR,[3,4,5,5.5,6,7.5,8.8,10,11.1,12])
ATA = A.transpose()*A
ATb = A.transpose()*b
ATA.solve_right(ATb)

(0.0367983733828612, -1.78815871355186)

r= matrix(QQ,[[1,0,2],[0,2,2],[-1,1,-1],[-1,2,0]])

y= matrix(QQ,[[3],[-3],[0],[-3]])

c= r.transpose()*r

v = r.transpose()*y

n = c.augment(v).echelon_form()

print n

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