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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 Jan. 17, 2020 by Teachoo
Ex 3.3, 2 If A = [■8(−1&2&3@5&7&9@−2&1&1)] and B= [■8(−4&1&−5@1&2&0@1&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&3@5&7&9@−2&1&1)] + [■8(−4&1&−5@1&2&0@1&3&1)] = [■8(−1+(−4)&2+1&3+(−5)@5+1&7+2&9+0@−2+1&1+3&1+1)] = [■8(−5&3&−2@6&9&9@−1&4&2)] Thus, A + B = [■8(−5&3&−2@6&9&9@−1&4&2)] (A + B)’ = [■8(−5&6&−1@3&9&4@−2&9&2)] Solving R.H.S A’ + B’ First we will calculate A’ and B’ A = [■8(−1&2&3@5&7&9@−2&1&1)] A’ =[■8(−1&5&−2@2&7&1@3&9&1)] B = [■8(−4&1&−5@1&2&0@1&3&1)] B’ = [■8(−4&1&1@1&2&3@−5&0&1)] Now, A’ + B’ = [■8(−1&5&−2@2&7&1@3&9&1)]+[■8(−4&1&1@1&2&3@−5&0&1)] = [■8(−1+(−4)&5+1&−2+1@2+1&7+2&1+3@3+(−5)&9+0&1+1)] =[■8(−5&6&−1@3&9&4@−2&9&2)] = L.H.S Hence Proved Ex 3.3, 2 If A = [■8(−1&2&3@5&7&9@−2&1&1)] and B= [■8(−4&1&−5@1&2&0@1&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&3@5&7&9@−2&1&1)] – [■8(−4&1&−5@1&2&0@1&3&1)] = [■8(−1−(−4)&2−1&3−(−5)@5−1&7−2&9−0@−2−1&1−3&1−1)] = [■8(−1+4&1&3+5@4&5&9@−3&−2&0)] = [■8(3&1&8@4&5&9@−3&−2&0)] Thus, A – B = [■8(3&1&8@4&5&9@−3&−2&0)] Now, (A – B)’ = [■8(3&4&−3@1&5&−2@8&9&0)] Solving R.H.S A’ – B’ First we will calculate A’ and B’ A = [■8(−1&2&3@5&7&9@−2&1&1)] A’ = [■8(−1&5&−2@2&7&1@3&9&1)] B = [■8(−4&1&−5@1&2&0@1&3&1)] B’ = [■8(−4&1&1@1&2&3@−5&0&1)] Now, A’ – B’ = [■8(−1&5&−2@2&7&1@3&9&1)]−[■8(−4&1&1@1&2&3@−5&0&1)] = [■8(−1−(−4)&5−1&−2−1@2−1&7−2&1−3@3−(−5)&9−0&1−1)] = [■8(−1+4&4&−3@1&5&−2@3+5&9&0)] = [■8(3&4&−3@1&5&−2@8&9&0)] = L.H.S Hence L.H.S = R.H.S Hence Proved