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Coordinate Vectors, Transition Matrix and Basis

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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.

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Solution Summary

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

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