Ex 3.3, 5 (ii) - Chapter 3 Class 12 Matrices

Last updated at April 16, 2024 by

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Ex 3.3, 5 For the matrices A and B, verify that (AB)′= B′A′, where (ii) A = [■8(0@1@2)] , B = [1 5 7] Solving L.H.S (AB)’ Finding AB AB = [■8(0@1@2)]_(3 × 1) 〖"[1 5 7]" 〗_(1 × 3) = [■8(0×1&0×5&0×7@1×1&1×5&1×7@2×1&2×5&2×7)]_(3×3) = [■8(𝟎&𝟎&𝟎@𝟏&𝟓&𝟕@𝟐&𝟏𝟎&𝟏𝟒)] Thus, AB = [■8(0&0&0@1&5&7@2&10&14)] So, (AB)’ = [■8(𝟎&𝟏&𝟐@𝟎&𝟓&𝟏𝟎@𝟎&𝟕&𝟏𝟒)] Solving R.H.S (B’ A’) Finding B’ B = [1 5 7] B’ = [■8(𝟏@𝟓@𝟕)] Also, A = [■8(0@1@2)] A’ = [0 1 2] B’ A’= [■8(1@5@7)]_(3×1) 〖"[0 1 2] " 〗_(1×3) = [■8(1×0&1×1&1×2@5×0&5×1&5×2@7×0&7×1&7×2)]_(3 × 3) = [■8(𝟎&𝟏&𝟐@𝟎&𝟓&𝟏𝟎@𝟎&𝟕&𝟏𝟒)] = L.H.S Hence L.H.S = R.H.S Hence proved

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.