# Misc 6 - Chapter 4 Class 12 Determinants

Last updated at Jan. 23, 2020 by Teachoo

Last updated at Jan. 23, 2020 by Teachoo

Transcript

Misc 6 Prove that |โ 8(a2&bc&ac+c2@a2+ab&b2&ac@ab&b2+bc&c2)| = 4a2b2c2 Solving L.H.S |โ 8(a2&bc&ac+c2@a2+ab&b2&ac@ab&b2+bc&c2)| = |โ 8(๐(๐)&๐(c)&๐(a+c)@๐(๐+๐)&๐(b)&๐(a)@๐(๐)&๐(b+c)&๐(c))| Taking out a common from C1 ,b common from C2 & c common from C3 = abc |โ 8(a&c&a+c@๐+๐&b&a@๐&b+c&c)| Applying C1โ C1 + C2 + C3 = abc |โ 8(a+๐+๐+๐&c&a+c@๐+๐+๐+๐&b&a@๐+๐+๐+๐&b+c&c)| = abc |โ 8(2a+2๐&c&a+c@2a+2๐&b&a@2๐+2๐&b+c&c)| = abc |โ 8(๐(๐+๐)&c&a+c@๐(๐+๐)&b&a@๐(๐+๐)&b+c&c)| Taking out 2 Common from C2 = 2a๐๐|โ 8((๐+๐)&c&a+c@(๐+๐)&b&a@(๐+๐)&b+c&c)| Applying C3โ C3 โ C1 = 2a๐๐|โ 8((๐+๐)&c&a+cโ(๐+๐)@(๐+๐)&b&aโ(a+b)@(๐+๐)&b+c&cโ(b+c))| = 2a๐๐|โ 8(๐+๐&c&๐@๐+๐&b&โ๐@๐+๐&b+c&โb)| Applying C2โ C2 โ C1 = 2abc |โ 8(๐+๐&cโ(๐+๐)&0@๐+๐&bโ(๐+๐)&โb@๐+๐&b+cโ(๐+๐)&โb)| = 2abc |โ 8(๐+๐&โ๐&0@๐+๐&โ๐&โ๐@๐+๐&0&โ๐)| Taking out โa common from C2, โb common from C3 = 2abc (โa) (โb) |โ 8(๐+๐&1&0@๐+๐&1&1@๐+๐&0&1)| Expanding Determinant along R1 = 2a2b2c ((a+c)|โ 8(1&1@0&1)|โ1|โ 8(๐+๐&1@๐+๐&1)|+0|โ 8(๐+๐&1@๐+๐&0)|) = 2a2b2c ((a+c)|โ 8(1&1@0&1)|โ1|โ 8(๐+๐&1@๐+๐&1)|+0) = 2a2b2c ((a + c) (1 โ 0) โ 1(a + b โ (b + c))) = 2a2b2c ((a + c) (1) โ 1 (a + b โ b โ c)) = 2a2b2c (a + c โ a + c) = 2a2b2c (2c) = 4a2b2c = R.H.S Hence proved

Miscellaneous

Misc 1

Misc. 2 Important Deleted for CBSE Board 2021 Exams only

Misc 3

Misc 4

Misc 5

Misc 6 Important You are here

Misc 7 Important

Misc 8

Misc 9

Misc 10

Misc 11 Important Deleted for CBSE Board 2021 Exams only

Misc 12 Important Deleted for CBSE Board 2021 Exams only

Misc. 13 Deleted for CBSE Board 2021 Exams only

Misc 14 Deleted for CBSE Board 2021 Exams only

Misc. 15 Important Deleted for CBSE Board 2021 Exams only

Misc. 16 Important

Misc 17 Important Deleted for CBSE Board 2021 Exams only

Misc 18

Misc 19 Important

Matrices and Determinants - Formula Sheet and Summary

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.