Linear Transformations and Coordinate

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Homework Statement



Let B be a basis of R^2 consisting of the vectors <5,2> and <1,5> and let R be the basis consisting of <2,3> and <1,2>

Find a matrix P such that [x]_r=P[x]_b for all x in R^2

Homework Equations



Ax=B?

The Attempt at a Solution




I attempted by using Ax=B as a format to solve for P, or x in the equation. I took the inverse of the column matrix of B because B is a basis, and if I am correct, a matrix's basis is defined as its coordinates ([x]_b).

I understand the geometrical interpretation of a linear transformation, yet I have no idea how to represent the transformation as a matrix. I would love an in depth description to approach similar exercises.
 
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Answers and Replies

  • #2
gabbagabbahey
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Homework Equations



Ax=B?

Not quite. The relevant equation in this case is the one given in the problem statement.

[tex][x]_r=P[x]_b[/tex]


How would you go about represented a general vector [itex]x[/itex] in the B-basis?
 

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