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

Last updated at June 8, 2023 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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.