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Ex 3.3
Ex 3.3, 2 You are here
Ex 3.3, 3
Ex 3.3, 4 Important
Ex 3.3, 5 (i)
Ex 3.3, 5 (ii)
Ex 3.3, 6 (i)
Ex 3.3, 6 (ii) Important
Ex 3.3, 7 (i)
Ex 3.3, 7 (ii) Important
Ex 3.3, 8
Ex 3.3, 9
Ex 3.3, 10 (i) Important
Ex 3.3, 10 (ii)
Ex 3.3, 10 (iii) Important
Ex 3.3, 10 (iv)
Ex 3.3, 11 (MCQ) Important
Ex 3.3, 12 (MCQ)
Last updated at March 16, 2023 by Teachoo
Ex 3.3, 2 If A = [■8(−1&2&[email protected]&7&[email protected]−2&1&1)] and B= [■8(−4&1&−[email protected]&2&[email protected]&3&1)] , then verify that (i) (A + B)’ = A’ + B’ Solving L.H.S (A + B)’ First we will calculate A + B A + B = [■8(−1&2&[email protected]&7&[email protected]−2&1&1)] + [■8(−4&1&−[email protected]&2&[email protected]&3&1)] = [■8(−1+(−4)&2+1&3+(−5)@5+1&7+2&[email protected]−2+1&1+3&1+1)] = [■8(−5&3&−[email protected]&9&[email protected]−1&4&2)] Thus, A + B = [■8(−5&3&−[email protected]&9&[email protected]−1&4&2)] (A + B)’ = [■8(−5&6&−[email protected]&9&[email protected]−2&9&2)] Solving R.H.S A’ + B’ First we will calculate A’ and B’ A = [■8(−1&2&[email protected]&7&[email protected]−2&1&1)] A’ =[■8(−1&5&−[email protected]&7&[email protected]&9&1)] B = [■8(−4&1&−[email protected]&2&[email protected]&3&1)] B’ = [■8(−4&1&[email protected]&2&[email protected]−5&0&1)] Now, A’ + B’ = [■8(−1&5&−[email protected]&7&[email protected]&9&1)]+[■8(−4&1&[email protected]&2&[email protected]−5&0&1)] = [■8(−1+(−4)&5+1&−[email protected]+1&7+2&[email protected]+(−5)&9+0&1+1)] =[■8(−5&6&−[email protected]&9&[email protected]−2&9&2)] = L.H.S Hence Proved Ex 3.3, 2 If A = [■8(−1&2&[email protected]&7&[email protected]−2&1&1)] and B= [■8(−4&1&−[email protected]&2&[email protected]&3&1)] , then verify that (ii) (A – B)’ = A’ – B’ Solving L.H.S (A – B)’ First we will calculate A – B A – B = [■8(−1&2&[email protected]&7&[email protected]−2&1&1)] – [■8(−4&1&−[email protected]&2&[email protected]&3&1)] = [■8(−1−(−4)&2−1&3−(−5)@5−1&7−2&9−[email protected]−2−1&1−3&1−1)] = [■8(−1+4&1&[email protected]&5&[email protected]−3&−2&0)] = [■8(3&1&[email protected]&5&[email protected]−3&−2&0)] Thus, A – B = [■8(3&1&[email protected]&5&[email protected]−3&−2&0)] Now, (A – B)’ = [■8(3&4&−[email protected]&5&−[email protected]&9&0)] Solving R.H.S A’ – B’ First we will calculate A’ and B’ A = [■8(−1&2&[email protected]&7&[email protected]−2&1&1)] A’ = [■8(−1&5&−[email protected]&7&[email protected]&9&1)] B = [■8(−4&1&−[email protected]&2&[email protected]&3&1)] B’ = [■8(−4&1&[email protected]&2&[email protected]−5&0&1)] Now, A’ – B’ = [■8(−1&5&−[email protected]&7&[email protected]&9&1)]−[■8(−4&1&[email protected]&2&[email protected]−5&0&1)] = [■8(−1−(−4)&5−1&−2−[email protected]−1&7−2&1−[email protected]−(−5)&9−0&1−1)] = [■8(−1+4&4&−[email protected]&5&−[email protected]+5&9&0)] = [■8(3&4&−[email protected]&5&−[email protected]&9&0)] = L.H.S Hence L.H.S = R.H.S Hence Proved