Solving Basis Problem in R2: Find P Matrix

[snoggerT]

Let B be the basis of R^2 consisting of the vectors :

(4,1) and (1,3)

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

*note: the vectors are columns, so in (4,1) the 4 is the top row and 1 is the bottom row.

Really not sure how to start this problem. Please help.

 

[snoggerT]

still looking for help on this problem.

 

[HallsofIvy]

How would (4, 1) and (1, 3), the B basis vectors, be written in the R basis?

The columns of matrix P will be those vectors.

 

[snoggerT]

Alright, got it. I feel stupid now though.