


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
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 You are here
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
Ex 4.2, 11 By using properties of determinants, show that: (i) |■8(a−b−c&2a&2a@2b&b−c−a&2b@2c&2c&c−a−b)| = (a + b + c)3 Solving L.H.S |■8(a−b−c&2a&2a@2b&b−c−a&2b@2c&2c&c−a−b)| Applying R1 → R1 + R2 + R3 = |■8(a−b−c+2𝑏+2𝑐&2a+b−c−a+2c&2a+2𝑏+𝑐−𝑎−𝑏@2b&b−c−a&2b@2c&2c&c−a−b)| = |■8(𝐚+𝐛+𝐜&𝐚+𝐛+𝐜&𝐚+𝒃+𝒄@2b&b−c−a&2b@2c&2c&c−a−b)| Taking common (a + b + c) from R1 = (a+b+c) |■8(1&1&1@2b&𝑏−𝑐−𝑎&2𝑏@2c&2𝑐&c−a−b)| Applying C1 → C1 – C2 = (a+b+c) |■8(𝟏−𝟏&1&1@2b−(b−c−a)&b−c−a&2𝑏@2c−2c&2𝑐&𝑐−𝑎−𝑏)| = (a+b+c) |■8(𝟎&1&1@b+c+a&b−c−a&2𝑏@0&2𝑐&𝑐−𝑎−𝑏)| Applying C2 → C2 – C3 = (𝑎+𝑏+𝑐)|■8(0&𝟏−𝟏&1@𝑏+𝑐+𝑎&𝑏−𝑐−𝑎−2𝑏&2𝑏@0&2𝑐−(𝑐−𝑎−𝑏)&𝑐−𝑎−𝑏)| = (𝑎+𝑏+𝑐)|■8(0&𝟎&1@𝑏+𝑐+𝑎&−𝑏−𝑐−𝑎&2𝑏@0&𝑎+𝑏+𝑐&𝑐−𝑎−𝑏)| Taking (a + b + c) common from C1 = (𝑎+𝑏+𝑐)(𝑎+𝑏+𝑐)|■8(0&0&1@1&−𝑏−𝑐−𝑎&2𝑏@0&(𝑎+𝑏+𝑐)&𝑐−𝑎−𝑏)| = (𝑎+𝑏+𝑐)2 |■8(0&0&1@1&−(𝒂+𝒃+𝒄)&2𝑏@0&(𝒂+𝒃+𝒄)&𝑐−𝑎−𝑏)| Taking common (a + b + c) from C2 = (𝑎+𝑏+𝑐)2(a+b+c) |■8(0&0&1@1&−1&2𝑏@0&1&𝑐−𝑎−𝑏)| Expanding determinant along R1 = (a + b + c)3 ( 0|■8(−1&2b@1&c−a−b)|−0|■8(1&2b@0&c−a−b)|+1|■8(1&−1@0&1)|) = (a + b + c)3 (0−0+1(1−0)) = (a + b + c)3 (1) = (a + b + c)3 Hence proved