InterviewSolution
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InterviewSolution
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What is `|{:(-a^(2),ab,ac),(ab,-b^(2),bc),(ac,bc,-c^(2)):}|` equal to ?A. `4a^(2) b^(2)`B. `4b^(2) c^(2)`C. `4c^(2) a^(2)`D. `4a^(2) b^(2) c^(2)` |
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Answer» Correct Answer - D We have, `Delta = |(a^(2),-ab,-ac),(-ab,b^(2),-bc),(ca,bc,-c^(2))|` `rArr Delta = abc |(a,-b,-c),(-a,b,-c),(a,b,-c)|` Taking a, b, c common from `T_(1), R_(2) and R_(3)` respectively `rArr Delta = a^(2) b^(2) c^(2) |(1,-1,-1),(-1,1,-1),(1,1,-1)|` Taking a,b, c common from `C_(1), C_(2) and C_(3)` respectively `rArr Delta = a^(2) b^(2) c^(2) |(1,0,0),(-1,0,-2),(1,2,0)|` Applying `C_(2) rarr C_(2) + C_(1), C_(3) rarr C_(3) + C_(1) `rArr Delta = 4a^(2) b^(2) c^(2)` |
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