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Coordinate Vectors, Transition Matrix and Basis

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. Thank you for your assistance.

Solution Summary

Coordinate vectors, transition matrices and bases are investigated. The solution is detailed and well presented.

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