NIMCET 2016 Question Paper with solutions

Question : 87 of 120

Marks: +1, -0

The system of equations
x + y + 2z = a
x + z = b
2x + y + 3z = c
has a solution if;

Solution:

Given system of equations is

x+y+2z=a

x+z=b

2x+y+3z=c

Applying matrix method, we get augmented matrix in the following form

=[\table 1,1,2,:,a;1,0,1,:,b;2,1,3,:,c]

=[\table1,1,2,:,a;0,1,1,:,a-b;0,1,1,:,2a-c]

[applying

\R_2→\R_1-\R_2

, and

\R_3→2\R_1-\R_3

]

=[\table1,1,2,:,a;0,1,1,:,a-b;0,0,0,:,a+b-c]

[applying

R_3→R_3-R_2

]
If solution exist, then

⇒a+b-c=0

⇒a+b=c

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