Consider the system of linear equations ...

Consider the system of linear equations in x, y, and z:
`(sin 3 theta) x-y+z=0`
`(cos 2 theta) x+4y+3z=0`
`2x+7y+7z=0`
Which of the following can be the values of `theta` for which the system has a non-trivial solution ?

`pi(n+1/3(-1)^(n))`

`pi(n+1/4(-1)^(n))`

`pi(n+1/6(-1)^(n))`

`(npi)/2`

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Consider the system of equations in x,y,z as x sin 3 theta -y +z=0, x cos 2 theta +4y+3z=0, 2x+7y +7z =0 . If this system has a non -trivial solution, then for integer n, values of theta are given by

`pi (n+((-1)^(1//2))/3)`

`pi (n+((-1)^(1//2))/4)`

`pi (n+((-1)^(1//2))/6)`

`(n pi)/2`

The given system will have infinite solutions for `a=2`

The number of integer values of `a` is `3` for the system to have nontrivial solutions.

For `a=1` there exists `theta` for which the system will have infinite solutions

For `a=3` there exists `theta` for which the system will have unique solutions

A unique solution

Finitely many solution

Infinitely many solutions

None of the above