Ex 3.4, 9 - Chapter 3 Class 12 Matrices (Term 1)

Transcript

Ex3.4, 9 Find the inverse of each of the matrices, if it exist [ 8(3&[email protected]&7)] Let A = [ 8(3&[email protected]&7)] We know that A = IA [ 8(3&[email protected]&7)]= [ 8(1&[email protected]&1)] A R1 R1 R2 [ 8( &10 [email protected]&7)]= [ 8(1 0&0 [email protected]&1)] A [ 8( &[email protected]&7)]= [ 8(1& [email protected]&1)] A R2 R2 2R1 [ 8(1&[email protected] ( )&7 2(3))]= [ 8(1& [email protected] 2(1)&1 2( 1))] A [ 8(1&[email protected] &7 6)]= [ 8(1& [email protected] 2&1+2)] A [ 8(1&[email protected] &1)]= [ 8(1& [email protected] 2&3)] A R1 R1 3R2 [ 8(1 3(0)& ( )@0&1)]= [ 8(1 3( 2)& 1 3(3)@ 2&3)] A [ 8(1 0& @0&1)]= [ 8(1+6& 1 [email protected] 2&3)] A [ 8(1& @0&1)]= [ 8(7& [email protected] 2&3)] A I = [ 8(7& [email protected] 2&3)] A This is similar to I = A-1 A Thus A-1 =[ 8(7& [email protected] 2&3)]