Ex 3.4, 17 - Find inverse [2 0 -1 5 1 0 0 1 3] - NCERT - Ex 3.4

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Ex3.4, 17 Find the inverse of each of the matrices, if it exists. [ 8(2&0& 1@5&1&0@0&1&3)] Let A =[ 8(2&0& 1@5&1&0@0&1&3)] We know that A = IA [ 8(2&0& 1@5&1&0@0&1&3)]= [ 8(1&0&0@0&1&0@0&0&1)] A R1 1/2 R1 , [ 8( / &0/2&( 1)/2@5&1&0@0&1&3)]= [ 8(1/2&0/2&0/2@0&1&0@0&0&1)] A [ 8( &0& 1/2@5&1&0@0&1&3)] = [ 8(1/2&0&0@0&1&0@0&0&1)] A R2 R2 5R1 [ 8(1&0& 1/2@ ( )&1 5(0)&0 5(( 1)/2)@0&1&3)] = [ 8(1/2&0&0@0 5(1/2)&1 5(0)&0 5(0)@0&0&1)] A [ 8(1&0& 1/2@ &1&5/2@0&0&3)]= [ 8(1/2&0&0@ 5/2&1&0@0&0&1)] A R3 R3 R2 [ 8(1&0& 1/2@0&1&5/2@ &0&3 5/2)]= [ 8(1/2&0&0@ 5/2&1&0@0 ( 5/2)&0 1&1 0)] A [ 8(1&0& 1/2@0&1&5/2@ &0&1/2)]= [ 8(1/2&0&0@ 5/2&1&0@5/2& 1&1)] A R3 2R3 [ 8(1&0& 1/2@0&1&5/2@2 0&2 0& / )]= [ 8(1/2&0&0@ 5/2&1&0@2 5/2&2 ( 1)&2(1))] A [ 8(1&0& 1/2@0&1&5/2@0&0& )]= [ 8(1/2&0&0@ 5/2&1&0@5& 2&2)] A R1 R1 + 1/2 R3 [ 8(1+1/2(0)&0+1/2(0)&( )/ + / ( )@0&1&5/2@0&0&1)]= [ 8(1/2+1/2(5)&0+1/2( 2)&0+1/2(2)@( 5)/2&1&0@5& 2&2)] A [ 8(1&0& @0&1&5/2@0&0&1)]= [ 8(3& 1&1@( 5)/2&1&0@5& 2&2)] A R2 R2 5/2 R3 [ 8(1&0&0@0 5/2(0)&1 5/2(0)& / / ( )@0&0&1)]= [ 8(3& 1&1@( 5)/2 5/2 (5)&1 5/2( 2)&0 5/2@5& 2&2)] A [ 8(1&0&0@0&1& @0&0&1)]= [ 8( 3& 1&1@( 30)/2&6& 5@5& 2&2)] A "I"= [ 8( 3& 1&1@ 15&6& 5@5& 2&2)] A This is similar to I = A-1A Thus, A-1 = [ 8(3& 1&1@ 15&6& 5@5& 2&2)]

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.