Course website: https://www.adampanagos.org/ala-applied-linear-algebra

We work with two different basis for R3 in this problem. The basis are denoted A and B. Similar to the previous video, we again compute a “change-of-coordinates” matrix that can transform a vector written in each basis to the other. However, since these are not the standard basis for R3, the computations to find the entries of the change-of-coordinates matrix require solving different systems of equations.

We conclude the problem by taking a vector written with respect to the basis A, e.g. [x]A, and transforming it to [x]B by multiplying by the computed change-of-coordinates matrix. We then transform back to [x]A and end up with the original vector as expected.

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