


Ex 4.2
Ex 4.2, 2 Important Deleted for CBSE Board 2022 Exams
Ex 4.2, 3 Deleted for CBSE Board 2022 Exams
Ex 4.2, 4 Deleted for CBSE Board 2022 Exams
Ex 4.2, 5 Important Deleted for CBSE Board 2022 Exams
Ex 4.2, 6 Important Deleted for CBSE Board 2022 Exams
Ex 4.2, 7 Important Deleted for CBSE Board 2022 Exams
Ex 4.2, 8 (i) Important Deleted for CBSE Board 2022 Exams
Ex 4.2, 8 (ii) Deleted for CBSE Board 2022 Exams You are here
Ex 4.2, 9 Important Deleted for CBSE Board 2022 Exams
Ex 4.2, 10 (i) Deleted for CBSE Board 2022 Exams
Ex 4.2, 10 (ii) Important Deleted for CBSE Board 2022 Exams
Ex 4.2, 11 (i) Deleted for CBSE Board 2022 Exams
Ex 4.2, 11 (ii) Important Deleted for CBSE Board 2022 Exams
Ex 4.2, 12 Important Deleted for CBSE Board 2022 Exams
Ex 4.2, 13 Important Deleted for CBSE Board 2022 Exams
Ex 4.2, 14 Important Deleted for CBSE Board 2022 Exams
Ex 4.2, 15 (MCQ) Important Deleted for CBSE Board 2022 Exams
Ex 4.2, 16 (MCQ) Deleted for CBSE Board 2022 Exams
Last updated at Aug. 18, 2021 by Teachoo
Ex 4.2, 8 By using properties of determinants, show that: (ii) |■8(1&1&1@a&b&c@a3&b3&c3)| = (a – b) (b – c) (c – a) (a + b + c) Solving L.H.S |■8(1&1&1@a&b&c@a3&b3&c3)| Applying C1 → C1 − C2 = |■8(𝟏−𝟏&1&1@a−b&b&c@𝐚𝟑 −𝐛𝟑&b3 &c3)| = |■8(𝟎&1&1@a−b&b&c@(𝐚 −𝐛)(𝐚𝟐+𝐛𝟐+𝐚𝐛) &b3&c3)| = |■8(0&1&1@𝐚−𝐛&b&c@(𝐚 −𝐛)(a2+b2+ab) &b3&c3)| Taking Common (a – b) from C1 = (a – b) |■8(0&1&1@1&b&c@(a2+b2+ab)&b3&c3)| Applying C2 → C2 − C3 = (a – b) |■8(0&𝟏−𝟏&1@1&b−c&c@(a2+b2+ab)&b3−c3&c3)| (x3 – y3 = (x – y)(x2 + y2 +xy)) = (a – b) |■8(0&𝟎&1@1&b−c&c@(a2+b2+ab)&(b−c)(b2+c2+bc)&c3)| Taking Common (b – c) from C2 = (a – b) (b – c) |■8(0&0&1@1&1&c@a2+b2+ab&b2+c2+bc&c3)| Expanding determinant along R1 = (a – b) (b – c) (0|■8(1&𝑐@𝑏2+𝑐2+𝑏𝑐&𝑐3)|−0|■8(1&1@𝑎2+𝑏2+𝑎𝑏&𝑐3)|+1|■8(1&1@𝑎2+𝑏2+𝑎𝑏&𝑏2+𝑐2+𝑏𝑐)|) = (a – b) (b – c) (0−0+1|■8(1&1@𝑎2+𝑏2+𝑎𝑏&𝑏2+𝑐2+𝑏𝑐)|) = (a – b) (b – c) (1((b2 + c2 + bc) – (a2 + b2 + ab)) = (a – b) (b – c) (b2 + c2 + bc – a2 – b2 – ab) = (a – b) (b – c) (c2 – a2 + bc – ab) = (a – b) (b – c) ((c – a) (c + a) + b (c – a)) = (a – b) (b – c) ((c – a) (c + a + b)) = (a – b) (b – c) ((c – a) (a + b + c)) = R.H.S Hence Proved