Ex 3.4, 1 - Chapter 3 Class 12 Matrices

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