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Misc 10 - Evaluate |1 x y 1 x+y y 1 x x+y| - Chapter 4 NCERT - Miscellaneous

Misc 10 - Chapter 4 Class 12 Determinants - Part 2

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Transcript

Misc 10 Evaluate 1﷮x﷮y﷮1﷮x+y﷮y﷮1﷮x﷮x+y﷯﷯ 1﷮x﷮y﷮1﷮x+y﷮y﷮1﷮x﷮x+y﷯﷯ Applying R1→ R1 – R2 = 𝟏−𝟏﷮x−x−y﷮y﷮1﷮x+y﷮y﷮1﷮𝑥﷮x+y﷯﷯ = 𝟎﷮−y﷮y﷮1﷮x+y﷮y﷮1﷮𝑥﷮x+y﷯﷯ Applying R2→ R2 – R3 = 0﷮−y﷮0﷮𝟏−𝟏﷮x+y−x﷮y−x−y﷮1﷮x﷮x+y﷯﷯ = 0﷮−y﷮0﷮𝟎﷮y﷮−x﷮1﷮𝑥﷮x+y﷯﷯ Expanding determinant along C1 = 0 𝑦﷮−𝑥﷮𝑥﷮𝑥+𝑦﷯﷯ – 0 −𝑦﷮𝑦﷮𝑥﷮𝑥+𝑦﷯﷯ + 1 −𝑦﷮0﷮𝑦﷮−𝑥﷯﷯ = 0 – 0 + 1 −𝑦﷮0﷮𝑦﷮−𝑥﷯﷯ = (0 – 0 + 1(xy)) = xy

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