Let S= { (1, 2), (0, 1)} and T= { (1, 1), (2,3) } be bases for R^2
Let the Vector V=(1,5) and the vector W=(5,4)
A. What are the coordinate vectors of V and W wrt to the basis T
B. What is the transition matrix P from T to S basis?
C. What are the coordinate vectors of V and W wrt to S (Using P from T to S basis)
D. Directly solve for the coordinate vectors of V and W WRT S
E. What is the transition matrix Q from the S to the T basis
If you can work out solutions to these sample problems it will allow me to have a basis for understanding how to go about solving these types of problems. Please work out solutions slowly.