Suppose T: R²→R³ is a linear transformation. Three vectors U, U₂ and U, are given below together with their images by T. Find T(W) for the given vector W.

U₁ = [ 1 ] U₂ = [ 3 ] U₃ = [ 1 ] w = [ 0 ] T(U₁) = [ 6 ] T(U₂) = [ 18 ] T(U₃) = [ 10 ]
[ 1 ] [ 3 ] [ 2 ] [ 2 ] [ 6 ] [ 18 ] [ 10 ]
[ 7 ] [ 18 ] [ 12 ]

T(W) = [ 0 ]
[ 0 ]
[ 0 ]