v1 = (0,3,−1) ,                                v2 = (1,2,0) ,

and let W be the plane spanned by v1 and v2. Consider the function

                                                            T : R3 → R3 where          T(x) = projW x ,

that is, T(x) is the projection of x onto the plane W; you may assume that T is a linear transformation.

i)        Evaluate T(5,0,10).

ii)      Find a basis for W ⊥ in R3.

iii)    Without calculation, write down the matrix of T with respect to the ordered basis {v1,v2,v3 }, where v3 is the basis element found in part (ii). By drawing a diagram, or otherwise, give reasons for your answer.

iv)    Hence or otherwise, find an expression for the matrix of T with respect to the standard basis in R3. You may leave your answer as a product of matrices without completing the calculation.