Ex 3.4, 8 - Chapter 3 Class 12 Matrices

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