Ex 3.2

Chapter 3 Class 12 Matrices
Serial order wise

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### Transcript

Ex 3.2, 14 Show that (i) [■8(5&−[email protected]&7)] [■8(2&[email protected]&4)] ≠ [■8(2&[email protected]&4)] [■8(5&−[email protected]&7)] Taking L.H.S [■8(5&−[email protected]&7)]_(2 × 2) [■8(2&[email protected]&4)]_(2 × 2) = [■8(5 × 2+(−1) × 3&5 × 1+(−1)× [email protected] × 2+7 × 3&6 × 1+7 × 4)]_(2 × 2) = [■8(10−3&5−[email protected]+21&6+28) ] = [■8(7&[email protected]&34)] Taking R.H.S [■8(2&[email protected]&4)]_(2 × 2) [■8(5&−[email protected]&7)]_(2 × 2) = [■8(2 × 5+1 × 6&2 × (−1)+1 × [email protected] × 5+4 × 6&3 × (−1)+4 × 7)]_(2 × 2) = [■8(10+6&−[email protected]+24&−3+28)] = [■8(16&[email protected]&25)] ≠ L.H.S Thus, L.H.S. ≠ R.H.S. Hence proved. Ex 3.2, 14 Show that (ii) [■8(1&2&[email protected]&1&[email protected]&1&0)][■8(−1&1&[email protected]&−1&[email protected]&3&4)] ≠[■8(−1&1&[email protected]&−1&[email protected]&3&4)][■8(1&2&[email protected]&1&[email protected]&1&0)] Taking L.H.S. [■8(1&2&[email protected]&1&[email protected]&1&0)]_(3 × 3) [■8(−1&1&[email protected]&−1&[email protected]&3&4)]_(3 × 3) = [■8(1×(⤶7−1)+2×0+3×2&1×1+2×(−1)+3×3&1×0+2×1+3×[email protected]×(⤶7−1)+1×0+0×2&0×1+1×(⤶7−1)+0×3&0×0+1×1+0×[email protected]×(⤶7−1)+1×0+0×2&1×1+1×(⤶7−1)+0×3&1×0+1×1+0×4)]_(3×3) = [■8(−1+0+6&1−2+9&[email protected]+0+0&0−1+0&[email protected]−1+0+0&1−1+0&0+1+0)] = [■8(5&8&[email protected]&−1&[email protected]−1&−1&1)] Taking R.H.S [■8(−1&1&[email protected]&−1&[email protected]&3&4)]_(3 × 3) [■8(1&2&[email protected]&1&[email protected]&1&0)]_(3 × 3) = [■8(−1×1+1×0+0×1&−1×2+1×1+0×1&−1×3+1×0+0×[email protected]×1+(−1)×0+1×1&0×2+(⤶7−1)×1+1×1&0×3+(−1)×0+1×[email protected]×1+(3)×0+4×1&2×2+3×1+4×1&2×3+(3)×0+4×0)]_(3×3) = [■8(−1+0+0&−2+1+0&−[email protected]+0+1&0−1+1&[email protected]+0+4&4+3+4&6+0+0)] = [■8(−1&−1&−[email protected]&0&[email protected]&11&6)] ≠ L.H.S ∴ L.H.S. ≠ R.H.S Hence proved

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#### Davneet Singh

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.