http://adampanagos.org
Course website: https://www.adampanagos.org/ala
Join the YouTube channel for membership perks:
https://www.youtube.com/channel/UCvpWRQzhm8cE4XbzEHGth-Q/join
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.
If you enjoyed my videos please "Like", "Subscribe", and visit http://adampanagos.org to setup your member account to get access to downloadable slides, Matlab code, an exam archive with solutions, and exclusive members-only videos. Thanks for watching!