Ex 3.3
Ex 3.3, 2
Ex 3.3, 3 You are here
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 April 16, 2024 by Teachoo
Ex 3.3,3 If A’ = [■8(3&4@−1&2@0&1)] and B =[■8(−1&2&1@1&2&3)] , then verify that (i) (A + B)’ = A’ + B’ Solving L.H.S (A + B)’ First finding A + B Given A’ = [■8(3&4@−1&2@0&1)] A = (A’)’ = [■8(3&4@−1&2@0&1)]^′ = [■8(3&−1&0@4&2&1)] Now, A + B = [■8(𝟑&−𝟏&𝟎@𝟒&𝟐&𝟏)] + [■8(−𝟏&𝟐&𝟏@𝟏&𝟐&𝟑)] = [■8(3+(−1)&−1+2&0+1@4+1&2+2&1+3)] = [■8(𝟐&𝟏&𝟏@𝟓&𝟒&𝟒)] So, (A + B)’ = [■8(2&5@1&4@1&4)] Solving R.H.S. (A’ + B’) Given A’ = [■8(𝟑&𝟒@−𝟏&𝟐@𝟎&𝟏)] Also B = [■8(−1&2&1@1&2&3)] B’ = [■8(−𝟏&𝟏@𝟐&𝟐@𝟏&𝟑)] A’ + B’ = [■8(3&4@−1&2@0&1)] + [■8(−1&1@2&2@1&3)] = [■8(3+(−1)&4+1@−1+2&2+2@0+1&1+3)] = [■8(𝟐&𝟓@𝟏&𝟒@𝟏&𝟒)] = L.H.S Hence, L.H.S = R.H.S Hence proved Ex 3.3, 3 If A’ = [■8(3&4@−1&2@0&1)] and B =[■8(−1&2&1@1&2&3)] , then verify that (ii) (A – B)’ = A’ – B’ Solving L.H.S (A – B)’ First finding A – B A – B = [■8(3&−1&0@4&2&1)] – [■8(−1&2&1@1&2&3)] = [■8(3−(−1)&−1−2&0−1@4−1&2−2&1−3)] = [■8(𝟑+𝟏&−𝟑&−𝟏@𝟑&𝟎&−𝟐)] = [■8(4&−3&−1@3&0&−2)] (A – B)’ = [■8(𝟒&𝟑@−𝟑&𝟎@−𝟏&−𝟐)] Solving R.H.S A’ – B’ Given A’ = [■8(3&4@−1&2@0&1)] A’ – B’ = [■8(3&4@−1&2@0&1)] – [■8(−1&1@2&2@1&3)] = [■8(3−(−1)&4−1@−1−2&2−2@0−1&1−3)] = [■8(3+1&3@−3&0@−1&−2)] = [■8(𝟒&𝟑@−𝟑&𝟎@−𝟏&−𝟐)] = L.H.S Hence, L.H.S = R.H.S Hence proved