Let U={U1, U2} and W{W1, W2} be bases for V, and let P be a matrix whose columns are,[u1]W and [u2]W ,which of the following equations is satisfied by P for all x in V?
1. [X ] U=P[ X ]W
2. [ X] W=P[ X ]U

In this context [x]U means the coordinate vector of vector x in the basis U. We are given that P has the coordinates of the vectors of basis U in the basis W. This means, that P translates the coordinates in U basis to the coordinates of a vector in the W basis. So, given a vector [x]U (coordinates in the U basis) then, by multiplying by P, we get the coordinates of x in the W basis. That is

[x]W = P[X]U.

Let U={U1, U2} and W{W1, W2} be bases for​ V, and let P be a matrix whose columns are,[u1]W and [u2]W ,which of the following equations is satisfied by P for all x in V? 1. [X ] U=P[ X ]W 2. [ X] W=P[ X ]U

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Let U={U1, U2} and W{W1, W2} be bases for V, and let P be a matrix whose columns are,[u1]W and [u2]W ,which of the following equations is satisfied by P for all x in V?
1. [X ] U=P[ X ]W
2. [ X] W=P[ X ]U