740.sagews

from numpy import *
from numpy.linalg import solve
 # 4 * x0 - 16 * x1 = 9
 # 13 * x0 - 8 * x1 = 23

a = array( [[4,-16], [16,-8]] )
b = array( [9, 23 ] )
x = solve( a, b ); x
print x
t=dot( a, x )
print t

[ 1.32142857 -0.23214286] [ 9. 23.]

# 6 * x0 + 20 * x1 = -22,4
# -5 * x0 - 0,12 * x1 = 1

c = array( [[6,20], [5,0.12]] )
d = array( [-22.4, 1 ] )
x = solve( c, d ); x
print x
s=dot( c, x )
print s

[ 0.22852538 -1.18855761] [-22.4 1. ]

from numpy import *
from numpy.linalg import solve
from numpy.linalg import inv
# -7 * x0 - 3 * x1 + 12 * x2 = 15
# 6 * x0 + 31 * x1 + 4 * x2 = 0,4
# 11 * x0 - 2 * x1 + 5 * x2 = 3

e = array( [[-7, -3, 12], [6,31,4], [11,-2,5] ] )
f = array( [15, 0.4, 3 ] )
x = solve( e, f ); x
print x
z=dot( e, x )
print z

[-0.23794058 -0.08178631 1.09075475] [ 15. 0.4 3. ]

# 1 * x0 - 4 * x1 + 2 * x2 = 1 
# -2 * x0 - 3 * x1 + 5 * x2 = 4 
# 3 * x0 +6 * x1 +7 * x2 = 5

g = array( [[1, -4, 2], [-2,-3,5], [3,6,7] ] )
h = array( [1, 4, 5 ] )
x = solve( g, h ); x
print x
u=dot( g, x )
print u

[-0.22543353 0.06936416 0.75144509] [ 1. 4. 5.]