InterviewSolution
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InterviewSolution
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Prove that `|((beta+gamma-alpha-delta)^4,(beta+gamma-alpha-delta)^2,1),((gamma+alpha-beta-delta)^4,(gamma+alpha-beta-delta)^2,1),((alpha+beta-gamma-delta)^4,(alpha+beta-gamma-delta)^2,1)|=-64(alpha-beta)(alpha-gamma)(alpha-delta)(beta-delta)(gamma-delta)` |
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Answer» Correct Answer - 64 Let `D= |{:((beta +gamma-alpha-delta)^(4),,(beta+gamma-alpha-delta)^(2),,1),((gamma+alpha-beta-delta)^(4),,(gamma+alpha-beta-delta)^(2),,1),((alpha+beta-gamma-delta)^(4),,(alpha+beta-gamma-delta)^(2),,1):}|` Applying `R_(1) toR_(1) -R_(3) ,R_(2) to R_(2)-R_(3)` `= |{:((beta+gamma-alpha-delta)^(4)-(alpha+beta-gamma-delta)^(4),,(beta+gamma-alpha-delta)^(2)-(alpha+beta-gamma-delta)^(2),,0),((gamma+delta-beta-delta)^(4)-(alpha+beta-gamma-delta)^(4),,(gamma+alpha-beta-delta)^(2)-(alpha+beta-gamma-delta)^(2),,0),((alpha+beta-gamma-delta)^(4),,(alpha+beta-gamma-delta)^(2),,1):}|` `=4(beta-delta)(gamma-alpha).4(alpha-delta)(gamma-beta)` `xx |{:((beta+gamma-alpha-delta)^(2)+(alpha+beta-gamma-delta)^(2),,1,,0),((gamma+alpha+beta-delta)^(2)+(alpha +beta-gamma-delta)^(2),,1,,0),((alpha+beta-gamma-delta)^(4),,(alpha+beta-gamma-delta)^(2),,1):}|` Applying `R_(1) to R_(1)-R_(2)` `=16(beta -delta)(gamma-alpha)(alpha-delta).4(gamma-delta)(beta-alpha)` `xx |{:(1,,0,,0),((gamma+alpha-beta-delta)^(2)+(alpha+beta-gamma-delta)^(2),,1,,0),((alpha+beta-gamma-delta)^(4),,(alpha+beta-gamma-delta)^(2),,1):}|` `=-64(alpha -beta) (alpha-gamma)(alpha-delta)(beta-gamma)(beta-delta)(gamma-delta)` |
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