Explore BrainMass
Share

# Linear transformations and subspaces

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

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.