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Ex 3.2, 15 - Find A2 - 5A + 6I if A = [2 0 1 - Class 12 Matrices - Ex 3.2

Ex 3.2, 15 - Chapter 3 Class 12 Matrices - Part 2

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Ex 3.2, 15 Find A2 5A + 6I if A = [ 8(2&0&1@2&1&3@1& 1&0)] Finding A2 A2 = AA = [ 8(2&0&1@2&1&3@1& 1&0)] [ 8(2&0&1@2&1&3@1& 1&0)] = [ 8(2(2)+0(2)+1(1)&2(0)+0(1)+1( 1)&2(1)+0(3)+1(0)@2(2)+1(2)+3(1)&2(0)+1(1)+3( 1)&2(1)+1(3)+3(0)@1(2)+ 1(2)+0(1)&1(0)+ 1(1)+0( 1)&1(1)+ 1(3)+0(0))] = [ 8(4+0+1&0+0 1&2+0+0@4+2+3&0+1 3&2+3+0@2 2+0&0 1+0&1 3+0)] = [ 8(5& 1&2@9& 2&5@0& 1& 2)] Now calculating A2 5A + 6I = [ 8(5& 1&2@9& 2&5@0& 1& 2)] 5 [ 8(2&0&1@2&1&3@1& 1&0)]+ 6 [ 8(1&0&0@0&1&0@0&0&1)] = [ 8(5& 1&2@9& 2&5@0& 1& 2)] [ 8(2 5&0 5&1 5@2 5&1 5&3 5@1 5& 1 5&0 5)] + [ 8(1 6&0 6&0 6@0 6&1 6&0 6@0 6&0 6&1 6)] = [ 8(5& 1&2@9& 2&5@0& 1& 2)] - [ 8(10&0&5@10&5&15@5& 5&0)] + [ 8(6&0&0@0&6&0@0&0&6)] = [ 8(5 10+6& 1 0+0&2 5+0@9 10+0& 2 5+6&5 15+0@0 5+0& 1+5+0& 2 0+6)] = [ 8(1& 1& 3@ 1& 1& 10@ 5&4&4)]

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.