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Ex 3.2
Ex 3.2, 2 (i)
Ex 3.2, 2 (ii) Important
Ex 3.2, 2 (iii)
Ex 3.2, 2 (iv)
Ex 3.2, 3 (i)
Ex 3.2, 3 (ii) Important
Ex 3.2, 3 (iii)
Ex 3.2, 3 (iv) Important
Ex 3.2, 3 (v)
Ex 3.2, 3 (vi) Important
Ex 3.2, 4
Ex 3.2, 5
Ex 3.2, 6
Ex 3.2, 7 (i)
Ex 3.2, 7 (ii) Important
Ex 3.2, 8
Ex 3.2, 9
Ex 3.2, 10
Ex 3.2, 11
Ex 3.2, 12 Important
Ex 3.2, 13 Important
Ex 3.2, 14 You are here
Ex 3.2, 15
Ex 3.2, 16 Important
Ex 3.2, 17 Important
Ex 3.2, 18
Ex 3.2, 19 Important
Ex 3.2, 20 Important
Ex 3.2, 21 (MCQ) Important
Ex 3.2, 22 (MCQ) Important
Last updated at March 22, 2023 by Teachoo
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