let T be a linear transformation given by T a b cab bc ac b

let T be a linear transformation given by T (a b c)=[a-b b+c a-c b] then T is

Let T be a linear transformation given by T b Then T is Select one: injective but not surjective surjective but not injective bijective neither surjective nor injective Check a-b b+ c

Solution

T(a b c)=T(a\' b\' c\') implies

[a-b b+c a-c b]=[a\'-b\' b\'+c\' a\'-c\' b\']

This gives b=b\',a=a\',c=c\'

SO, T is injective

, But T is not surjective as T is a map from 3 dimensional space to 4 dimensional space