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The system of equations (sin 3 theta) x ...

The system of equations `(sin 3 theta) x - y+z=0,(cos 2 theta)x+4y+3z=0, 2x+7y+7z=0` has non trivial solutions if

A

`n pi +(-1)^(n)pi//6, AA n in Z`

B

`n pi+(-1)^(n) pi//3, AA n in Z`

C

`n pi+(-1)^(n)pi//9, AA n in Z`

D

`n pi +(-1)^(n)(pi)/12, AA n in Z`

Text Solution

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The correct Answer is:
A
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Consider the system of liner equations in x, y and z ( sin 3 theta ) x - y + x = 0 ( cos 2 theta ) x + 4 y + 3 z = 0 2 x + 7 y + 7 z = 0 which of the following can be the values of theta for which the system has a non-trivial solution

Knowledge Check

  • A set of values of theta for which the system of equations (sin 3theta ) x +4y+3z=0,2x+7y+7z=0 has non -trivial solutions is

    A
    `(n+1)^(pi)/(2)+(-1)^(n)(pi)/(4)` (here n is any integer)
    B
    `(n-1)^(pi)/(2)+(-1)^(n)(pi)/(4)` (here n is any integer)
    C
    `(npi)/(2)+(-1)^(n)(pi)/(6)` ( here n is any integer )
    D
    `npi +(-1)^(n)(pi)/(6)` ( here n is any integer )

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  • If the system of equations lambdax + 3y + z = 0 , 4x+lambday+3z=0, 2x+3y+lambdaz=0 has non-trival solution, then lambda =

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