

Subscribe to our Youtube Channel - https://you.tube/teachoo
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. 2 Important Not in Syllabus - CBSE Exams 2021 You are here
Misc 3
Misc 4
Misc 5
Misc 6 Important
Misc 7 Important
Misc 8
Misc 9
Misc 10
Misc 11 Important Not in Syllabus - CBSE Exams 2021
Misc 12 Important Not in Syllabus - CBSE Exams 2021
Misc. 13 Not in Syllabus - CBSE Exams 2021
Misc 14 Not in Syllabus - CBSE Exams 2021
Misc. 15 Important Not in Syllabus - CBSE Exams 2021
Misc. 16 Important
Misc 17 Important Not in Syllabus - CBSE Exams 2021
Misc 18
Misc 19 Important
Matrices and Determinants - Formula Sheet and Summary
About the Author