Ex 3.4, 6 - Chapter 3 Class 12 Matrices (Term 1)

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