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Last updated at Jan. 23, 2020 by Teachoo

Transcript

Misc 2 Without expanding the determinant, prove that |■8(a&a2&bc@b&b2&ca@c&c2&ab)| = |■8(1&a2&a3@1&b2&b3@1&c2&c3)| Solving L.H.S |■8(a&a2&bc@b&b2&ca@c&c2&ab)| Multiplying and dividing by abc = abc/abc |■8(a&a2&bc@b&b2&ca@c&c2&ab)| Multiplying a to R1, b to R2 & c to R3 = 1/abc |■8(a(𝑎)&𝑎(a2)&a(bc)@b(𝑏)&b(b2)&b (ca)@c(𝑐)&𝑐(c2)&c (ab))| Multiplying a to R1, b to R2 & c to R3 = 1/abc |■8(a(𝑎)&𝑎(a2)&a(bc)@b(𝑏)&b(b2)&b (ca)@c(𝑐)&𝑐(c2)&c (ab))| = 1/abc |■8(a2&a3&𝑎𝑏𝑐@b2&b3&𝑎𝑏𝑐@c2&c3&𝑎𝑏𝑐)| Taking abc common from C3 = 𝑎𝑏𝑐/𝑎𝑏𝑐 |■8(a2&a3&1@b2&b3&1@c2&c3&1)| = |■8(a2&a3&1@b2&b3&1@c2&c3&1)| Interchange C1 ↔ C3 = (–1) |■8(1&a3&a2@1&b3&b2@1&c3&c2)| Interchange C2 ↔ C3 = (–1) (–1) |■8(1&a2&a3@1&b2&b3@1&c2&c3)| = |■8(1&a2&a3@1&b2&b3@1&c2&c3)| = R.H.S. Hence Proved We know that If any two row or column of a determinant are interchanged, then sign of determinant changes.

Miscellaneous

Misc 1

Misc. 2 Important You are here

Misc 3

Misc 4

Misc 5

Misc 6 Important

Misc 7 Important

Misc 8

Misc 9

Misc 10

Misc 11 Important

Misc 12 Important

Misc. 13

Misc 14

Misc. 15 Important

Misc. 16 Important

Misc 17 Important

Misc 18

Misc 19 Important

Matrices and Determinants - Formula Sheet and Summary

Chapter 4 Class 12 Determinants

Serial order wise

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.