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Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


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Misc 5 If A = [■8(3&1@−1&2)] , show that A2 – 5A + 7I = O First calculating A2 A2 = A.A A2 = [■8(𝟑&𝟏@−𝟏&𝟐)] [■8(𝟑&𝟏@−𝟏&𝟐)] = [■8(3(3)+1(−1)&3(1)+1(2)@−1(3)+2(−1)&−1(1)+2(2))] = [■8(9−1&3+2@−3−2&−1+4)] = [■8(𝟖&𝟓@−𝟓&𝟑)] Now calculating A2 – 5A – 7I = [■8(𝟖&𝟓@−𝟓&𝟑)] – 5 [■8(𝟑&𝟏@−𝟏&𝟐)] + 7 [■8(𝟏&𝟎@𝟎&𝟏)] = [■8(8&5@−5&3)] – [■8(5(3)&5(1)@5(−1)&5(2))] + [■8(7(1)&7(0)@7(0)&7(1))] = [■8(8&5@−5&3)] – [■8(15&5@−5&10)] + [■8(7&0@0&7)] = [■8(8−15+7&5−5+0@−5−(−5)&3−10+7)] = [■8(𝟎&𝟎@𝟎&𝟎)] = O = R.H.S. Since L.H.S = R.H.S Hence proved

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.