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Misc 14 - Using properties of determinants, prove - Class 12 - Miscellaneous

Misc 14 - Chapter 4 Class 12 Determinants - Part 2
Misc 14 - Chapter 4 Class 12 Determinants - Part 3


Transcript

Misc 14 Using properties of determinants, prove that: 1﷮1+p﷮1+p+q﷮2﷮3+2p﷮4+3p+2q﷮3﷮6+3p﷮10+6p+3q﷯﷯ = 1 Taking L.H.S 1﷮1+p﷮1+p+q﷮2﷮3+2p﷮4+3p+2q﷮3﷮6+3p﷮10+6p+3q﷯﷯ Applying R2→ R2 – 2R1 = 1﷮1+p﷮1+p+q﷮𝟐−𝟐(𝟏)﷮3+2p−2(1+p)﷮4+3𝑝+2𝑝−2(1+𝑝+𝑞)﷮3﷮6+3p−2﷮10+6p+3q﷯﷯ = 1﷮1+p﷮1+p+q﷮𝟎﷮1﷮2+𝑝﷮3﷮6+3p﷮10+6p+3q﷯﷯ Applying R3→ R3 – 3R2 = 1﷮1+p﷮1+p+q﷮0﷮1﷮2+p﷮𝟑−𝟑(𝟏)﷮6+3𝑝−3(1+𝑝)﷮10+6𝑝+3𝑞−3(1+𝑝+𝑞)﷯﷯ = 1﷮1+p﷮1+p+q﷮0﷮1﷮2+p﷮𝟎﷮3﷮7+3𝑝﷯﷯ Expanding determinant along C1 = 1 1﷮2+p﷮3﷮7+3p﷯﷯ – 0 1+𝑝﷮2+p﷮3﷮7+3p﷯﷯ + 0 1+𝑝﷮1+p+q﷮1﷮2+p﷯﷯ = 1 1﷮2+p﷮3﷮7+3p﷯﷯ – 0 + 0 = 1 (7 + 3p – 3 (2 + p)) = 7 + 3p – 6 – 3p = 1 = R.H.S Hence Proved

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.