Let T : P₂ → R² be a linear transformation defined by T(p) = [(0)]. O {ait a₁ € R} O {azt²a2 € R} O fait + a2t² lai, a2 € R} O fait + azt² la₁ + a₂ = 0} O P₂2 Find the kernel of T.

Let T: P₂ → R² be the linear transformation defined by T(a₁x² + ₂x + α3) = [3 sas]: T(6x² + 4x + 5) = -2a1 3a2 + 6a3 Ex: 5 8 Ex: 5

Let T : U → V be a linear transformation. Use the rank-nullity theorem to complete the information in the table below. U R R" dim(U) 5 Ex: 5 Ex: n+2 rank(T) nullity(T) 4 Ex: 5 Ex: n+2 Ex: 5 6 5

17. Let T R² R² be a linear transformation that maps [1] [3] 3 Tis linear to find the images under T of 3u, 2v, and 3u + 2v. u= into and maps v = into Use the fact that