v 1 = (0 , 3 , 1) , v 2 = (1 , 2 , 0) , and let W be the plane spanned by v 1 and v 2 .

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.
 
“Looking for a Similar Assignment? Get Expert Help at an Amazing Discount!”

"Is this qustion part of your assignmentt? We will write the assignment for you. click order now and get up to 40% Discount"