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The following system of linear equations 7x2y+6z=0, 3x+2y+4z=0, x6y2z=0has

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a
Infinitely many solutions, satisfying x=2y
b
Only the trivial solution
c
Infinitely many solution, satisfying 2y=z
d
No solution

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detailed solution

Correct option is A

We have7−263241−6−2=720+2−10+6−20=140−140=0 ⇒Infinite non-trivial solutions exists .   Also equations (1)-(2)+(3)⇒5x-10y=0 ⇒x=2y


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