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Ex 4.5
Ex 4.5, 2
Ex 4.5, 3 Important
Ex 4.5, 4 Important
Ex 4.5, 5
Ex 4.5, 6 Important
Ex 4.5, 7
Ex 4.5, 8
Ex 4.5, 9
Ex 4.5, 10 Important
Ex 4.5, 11 Important
Ex 4.5, 12 You are here
Ex 4.5, 13
Ex 4.5, 14 Important
Ex 4.5, 15 Important
Ex 4.5, 16
Ex 4.5, 17 (MCQ) Important
Ex 4.5, 18 (MCQ) Important
Last updated at March 30, 2023 by Teachoo
Ex 4.5, 12 Let A = [■8(3&[email protected]&5)] and B = [■8(6&[email protected]&9)] verify that (AB)-1 = B-1 A-1 Taking L.H.S (AB)–1 First calculating AB AB = [■8(3&[email protected]&5)] [■8(6&[email protected]&9)] = [■8(3(6)+7(7)&3(8)+7(9)@2(6)+5(7)&2(8)+5(9))] = [■8(18+49&[email protected]+35&16+45)] = [■8(67&[email protected]&61)] Now, (AB)-1 = 1/(|AB|) adj (AB) exists if |AB| ≠ 0 |AB| = |■8(67&[email protected]&61)| = 67 (61) – 47(87) = 4087 – 4089 = –2 Since |AB| ≠ 0 ∴ (AB)–1 exists Now, AB = [■8(67&[email protected]&61)] adj (AB) = [■8(67&[email protected]&61)] = [■8(61&−[email protected]−47&67)] Thus, (AB)–1 = 1/(|AB|) adj (AB) Putting values = 1/(−2) [■8(61&−[email protected]−47&67)] Taking R.H.S B-1A-1 First Calculating B-1 B–1 = 1/(|B|) adj (B) exist if |B|≠ 0 Now, |B| = |■8(6&[email protected]&9)| = 6(9) – 7(8) = 54 – 56 = –2 Since |B|≠ 0 ∴ B–1 exists Now, B = [■8(6&[email protected]&9)] adj B = [■8(6&[email protected]&9)] = [■8(9&−[email protected]−7&6)] Thus, B–1 = 1/(|B|) adj (B) = 1/(−2) [■8(9&−[email protected]−7&6)] Calculating A-1 A-1 = 1/(|A|) adj (A) exist if |A| ≠ 0 |A| = |■8(3&[email protected]&5)| = 15 – 14 = 1 Since |A| ≠ 0, A-1 exists A = [■8(3&[email protected]&5)] adj A = [■8(3&[email protected]&5)] = [■8(5&−[email protected]−2&3)] So, A–1 = 1/(|A|) adj (A) = 1/1 [■8(5&−[email protected]−2&3)] = [■8(5&−[email protected]−2&3)] Now B-1 A-1 = (−1)/2 [■8(9&−[email protected]−7&6)] [■8(5&−[email protected]−2&3)] = (−1)/2 [■8(9(5)+( –8)( –2)&9(−7)+(−8)(3)@ –7(5)+6( –2)&−7(−7)+6(3))] = (−1)/2 [■8(45+16&−63−[email protected]−35−12&49+18)]