B1) This question concerns the following two subsets of :
(a) Show that , and find a vector in that does not belong to T. 
(b) Show that T is a subspace of . 
(c) Show that S is a basis for T, and write down the dimension of T. 
(d) Find an orthogonal basis for T that contains the vector . 
(e) Express the vector of T as a linear combination of the vectors in your orthogonal basis for T. 
B2 This question concerns the function t given by the rule
(a) Use the strategy in Unit 4, section 1, to show that t is a linear transformation. 
(b) Write down the matrix for t with respect to the standard basis in both the domain and codomain. 
(c) Determine the matrix of t with respect to the domain basis S of and the standard basis in the codomain. 
(d) Determine the matrix of t with respect to the domain basis S of basis and codomain basis of U. 
(e) Find the kernel of t, and states its dimension. 
(f) Let be a linear transformation given by . Determine the matrix of m and with respect to the standard basis in both the domain and the codomain. 
Please see the attached file for the fully formatted problems.
Linear transformations and subspaces are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.