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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&[email protected]&1&[email protected]& 1&0)] Finding A2 A2 = AA = [ 8(2&0&[email protected]&1&[email protected]& 1&0)] [ 8(2&0&[email protected]&1&[email protected]& 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&[email protected]+2+3&0+1 3&[email protected] 2+0&0 1+0&1 3+0)] = [ 8(5& 1&[email protected]& 2&[email protected]& 1& 2)] Now calculating A2 5A + 6I = [ 8(5& 1&[email protected]& 2&[email protected]& 1& 2)] 5 [ 8(2&0&[email protected]&1&[email protected]& 1&0)]+ 6 [ 8(1&0&[email protected]&1&[email protected]&0&1)] = [ 8(5& 1&[email protected]& 2&[email protected]& 1& 2)] [ 8(2 5&0 5&1 [email protected] 5&1 5&3 [email protected] 5& 1 5&0 5)] + [ 8(1 6&0 6&0 [email protected] 6&1 6&0 [email protected] 6&0 6&1 6)] = [ 8(5& 1&[email protected]& 2&[email protected]& 1& 2)] - [ 8(10&0&[email protected]&5&[email protected]& 5&0)] + [ 8(6&0&[email protected]&6&[email protected]&0&6)] = [ 8(5 10+6& 1 0+0&2 [email protected] 10+0& 2 5+6&5 [email protected] 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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.