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In the previous video, we were provided a basis B and the vector x. We then computed the vector [x]B, the representation of x with respect to the basis B.
In this problem we construct a "change-of-coordinates" matrix P that can transform any vector written with respect to basis B back to the standard basis. This transformation takes place by the matrix-vector multiplication P*[x]B. For the particular values of [x]B and x we've considered previously, we check that indeed P*[x]B = x as expected.
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