InterviewSolution
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InterviewSolution
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Let `lambda` and `alpha` be real. Then the numbers of intergral values `lambda` for which the system of linear equations `lambdax +(sin alpha) y+ (cos alpha) z=0` `x + (cos alpha) y+ (sin alpha) z=0` `-x+(sin alpha) y -(cos alpha) z=0` has non-trivial solutions is |
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Answer» Correct Answer - D The given system has non=trivial solution if `|{:(lambda,,sin alpha,,cos alpha),(1,,cos alpha,,sin alpha),(-1,,sin alpha,,-cos alpha):}|=0` By expanding the determinant along first column we get `lambda =sin 2alpha +cos 2alpha` We know that `-sqrt(2) le sin 2alpha + cos 2 alpha le sqrt(2)` `:. -sqrt(2) le lambda le sqrt(2)` hence integral values of `lambda` are -1 ,0 and 1 |
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