InterviewSolution
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InterviewSolution
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if w is a complex cube root to unity then value of ` Delta =|{:(a_(1)+b_(1)w,,a_(1)w^(2)+b_(1),,c_(1)+b_(1)bar(w)),(a_(2)+b_(2)w,,a_(2)w^(2)+b_(2),,c_(2)+b_(2)bar(w)),(a_(3)+b_(3)w,,a_(3)w^(2)+b_(3),,c_(3)+b_(3)bar(w)):}|` is |
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Answer» Correct Answer - A `Delta =|{:(a_(1)+b_(1)w,,a_(1)w^(2)+b_(1),,c_(1)+b_(1)hat(w)),(a_(2)+b_(2)w,,a_(2)w^(2)+b_(2),,c_(2)+b_(2)hat(w)),(a_(3)+b_(3)w,,a_(3)w^(2)+b_(3),,c_(3)+b_(3)hat(w)):}|` `" Operating " C_(2) to wC_(2) ` we have `Delta =(1)/(w) |{:(a_(1)+b_(1)w,,a_(1)w^(2)+b_(1),,c_(1)+b_(1)hat(w)),(a_(2)+b_(2)w,,a_(2)w^(2)+b_(2),,c_(2)+b_(2)hat(w)),(a_(3)+b_(3)w,,a_(3)w^(2)+b_(3),,c_(3)+b_(3)hat(w)):}|` `=(1)/(w)|{:(a_(1)+b_(1)w,,a_(1)+b_(1)w,,c_(1)+b_(1)hat(w)),(a_(2)+b_(2)w,,a_(2)+b_(2)w,,c_(2)+b_(2)hat(w)),(a_(3)+b_(3)w,,a_(3)+b_(3)w,,c_(3)+b_(3)hat(w)):}|` `=0` |
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