Question

1. LetT :R3→R3 . Show that if
T ([c1 c2 c3]) = c1T ([1 0 0]) + c2T([0 1 0]) + c3T ([0 0 1]) for c1, c2, c3 ∈ R

then T satisfies

T(a⃗v1+b⃗v2)=aT(⃗v1)+bT(⃗v2), for a, b ∈R and⃗ v1, v2 ∈R .