Consider: x + y + z = 2 x + 3y + 3z = 0 x+ 3y+ 6z = 3 Use process of Gauss Elimination to solve the equation?

Question

Consider:
x + y + z = 2
x + 3y + 3z = 0
x+ 3y+ 6z = 3

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Answer 1 · 2018-04-11T17:59:43

#x=3, y=-2, z= 1#

We write the augmented matrix

#((1,1,1,|,2),(1,3,3,|,0),(1,3,6,|,3))#

Carrying out the row operations

#R_2 larr R_2-R_1,R_3 larr R_3-R_1# :

#((1,1,1,|,2),(0,2,2,|,-2),(0,2,5,|,1))#

#R_3 larr R_3-R_2# :

#((1,1,1,|,2),(0,2,2,|,-2),(0,0,3,|,3))#

Now we carry out back-substitution :

#3z=3 implies z=1#
#2y+2z=-2 implies 2y=-4 implies y=-2#
#x+y+z=2 implies x = 3#