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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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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.