Let SV1V2V3 be a set of linearly independent vectors in R3 F

Let S=V1,V2,V3 be a set of linearly independent vectors in R3. Find a linear transformation of T from R3 into R3 that the set (tV1,tV2,tV3)) is linearly dependent

Solution

Since no restriction on T is given in the problem. WE take T to be the identity transformation.

So,

T(V1)=V1,T(V2)=V2,T(V3)=V3

{T(V1),T(V2),T(V3)}={V1,V2,V3}

Hence the set {T(V1),T(V2),T(V3)} is linearly independent since S is linearly independent set of vectors.