Let v be a vector in R" and define a function T, : R" → R by T,(x) = x v. (a) Show that T, is a linear transformation. (b) Find the standard matrix for Ty, where v = = (1, 1, 1).

Let B= (b,, b,, b,} and D= (d,, d,} be bases for vector spaces V and W, respectively. Let T :V- W be a linear transformation with the following properties. T(b,) = - 3d, +2d2, T(b2) = - 4d, + 4d2, T(b3) = 5d2 Find the matrix for T relative to B and D. The matrix for T relative to B and D isO.

Could you explain how to show this in detail?