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

  1. Chapter 3 Class 12 Matrices
  2. Serial order wise
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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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