The value of 0 for which the system of equations
(sin 3 
)x - 2y + 3z = 0, (cos 2 
)x + 8y - 7z = 0 and 2x + 14y - 11z = 0 has a non-trivial solution, is (here, n 
Z)
Text Solution
Verified by ExpertsA
The system of equations has a non-trivial solution if and only if 
Applying R 2 
R2 + 4Ri, R 3 
R 3 + 7R 1 , weget,
Expanding along C 2 , we get,
2 (cos 2 
+ 4sin3 
) - (2 + 7 sin 3 
) = 0
2- 2 cos 2 
- sin 3 
= 0
4sin 2 
- (3 sin 
- 4sin 3 
) = 0
sin 
(4sin 2 
+ 4sin 
- 3) = 0
sin 
(2sin 
- 1) (2sin 
+ 3) = 0
sin 
= 0 or sin 
= 1/2.
[ sin 
= -3/2 is not possible]
For, 
the system of equations has a non-trivial solution.
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