Transpose of a matrix
Last updated at Aug. 16, 2021 by Teachoo
Ex 3.3, 5 For the matrices A and B, verify that (AB) = B A where (i) A = [ 8(1@ 4@3)] , B = [-1 2 1] Taking L.H.S (AB) Finding AB first AB =[ 8(1@ 4@3)]_(3 1) "[ 1 2 1] " _(1 3) = [ 8(1 ( 1) &1 2&1 1@ 4 ( 1)& 4 2& 4 1@3 ( 1)&3 2&3 1)]_(3 3) = [ 8( 1&2&1@4& 8& 4@ 3&6&3)] AB = [ 8( 1&2&1@4& 8& 4@ 3&6&3)] Now, (AB) = [ 8( 1&4& 3@2& 8&6@1& 4&3)] Taking R.H.S B A Finding B , A Given B = [ 1 2 1] B = "[" "1 2 1]" ^ = [ 8( 1@2@1)] Given A = [ 8(1@ 4@1)] A = [1 4 1] Now, B A = [ 8( 1@2@1)]_(3 1) "[1 4 3]" _(1 3) = [ 8( 1 1& 1 ( 4)& 1 3@2 1&2 ( 4)&2 3@1 1&1 ( 4)&1 3)]_(3 3) = [ 8( 1&4& 3@2& 8&6@1& 4&3)] = L.H.S Hence L.H.S = R.H.S Hence proved