GATE Civil Engineering (CE) 2020 Shift 1 Solved Paper

Question : 60 of 65

Marks: +1, -0

Consider the system of equations

[\table 1 , 3 , 2 ; 2 , 2 , -3 ; 4 , 4 , -6 ; 2 , 5 , 2][\table {x}_{1} ; {x}_{2} ; {x}_{3}]=[\table 1 ; 1 ; 2 ; 1]

The value of

x_{3}

(round off to the nearest integer) is

Solution:

Solving the above matrix by multiplication

x_{1}+3 x_{2}+2 x_{3}=1

.....(i)

2 x_{1}+2 x_{2}-3 x_{3}=1

.....(2)

4 x_{1}+4 x_{2}-6 x_{3}=2

.....(3)

2 x_{1}+5 x_{2}+2 x_{3}=1

........(4)
Solving equation (1) and (2) eliminating

x_1

we get,

Solving equation (3) and (4) eliminating

x_1

, we get

Solving equation (5) and (6) we get

4 x_{2}+7 x_{3}=1

-6 x_{2}-10 x_{3}=0

x_3 = 3

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