Ex 3.3
Ex 3.3, 2
Ex 3.3, 3
Ex 3.3, 4 Important
Ex 3.3, 5 (i) You are here
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, 5 For the matrices A and B, verify that (AB)′ = B’A’ where (i) A = [■8(1@− 4@3)] , B = [-1 2 1] Solving L.H.S (AB)’ Finding AB first AB =[■8(𝟏@−𝟒@𝟑)]_(𝟑×𝟏) 〖"[−1 2 1] " 〗_(𝟏×𝟑) = [■8(1×(−1) &1×2&1×1@−4×(−1)&−4×2&−4×1@3×(−1)&3×2&3×1)]_(3×3) = [■8(−𝟏&𝟐&𝟏@𝟒&−𝟖&−𝟒@−𝟑&𝟔&𝟑)] AB = [■8(−1&2&1@4&−8&−4@−3&6&3)] Now, (AB)’= [■8(−𝟏&𝟒&−𝟑@𝟐&−𝟖&𝟔@𝟏&−𝟒&𝟑)] Solving R.H.S B’ A’ Finding B’ , A’ Given B = [− 1 2 1] B’ = 〖"[" − "1 2 1]" 〗^′= [■8(−𝟏@𝟐@𝟏)] Given A = [■8(1@−4@1)] A’ = [1 − 4 1] Now, B’ A’ = [■8(−𝟏@𝟐@𝟏)]_(𝟑×𝟏) 〖"[1 − 4 3]" 〗_(𝟏×𝟑) = [■8(−1×1&−1×(−4)&−1×3@2×1&2×(−4)&2×3@1×1&1×(−4)&1×3)]_(3 × 3) = [■8(−𝟏&𝟒&−𝟑@𝟐&−𝟖&𝟔@𝟏&−𝟒&𝟑)] = L.H.S Hence L.H.S = R.H.S Hence proved