import numpy as np

A = np.array([[3.0,-0.1,-0.2],[0.1,7.0,-0.3],[0.3,-0.2,10.2]])

B = np.array([[7.85],[-19.3],[71.4]])


##########################################################################################
aMat = np.hstack([A, B]) # combine matrix A and B to create augmented matrix

nRows = len(aMat[:,0]) # get how many rows
nCols = len(aMat[0,:]) # get how many columns

#print 'Augmented Matrix'
#print aMat
#print '*****************************************************************************'

# forward elimination

#Matrix in Python [row,col]

#1) keep row0
#2) from row1 ; calculate scale factor c= aMat[1,0]/aMat[0,0]
#3) find new row1 ; row1_new = row1 - c*row0

#4) from row2 ; calculate scale factor c=aMat[2,0]/aMat[0,0]
#5) find new row2 ; row2_new = row2 - c*row0

#Repeat step in row1 and row2


for row in range(1,3):
    c = aMat[row,0]/aMat[0,0]

    for col in range(4):
        aMat[row,col] =  aMat[row,col]-(aMat[0,col]*c)
print "Step1: "
print aMat

#Step2

for row in range(2,3):
    c = aMat[row,1]/aMat[1,1]

    for col in range(4):
        aMat[row,col] =  aMat[row,col]-(aMat[1,col]*c)
print "Step2: "
print aMat