Linear Algebra Example Problems - Change of Coordinates Matrix #2

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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.

[tomificationness]

really appreciate that you don't waste time writing it out.

[marcusbluestone]

Honestly, you saved my life. Super clear explanation, beautiful handwriting, no very simple. God bless your soul.

[nathan]

So helpful, exactly what I was looking for. Presentation is clear and very neat. Thanks.

[aadilmufti]

You and 3Blue1Brown are all that is needed to learn linear algebra. I like to watch his videos to get the theoretical grasp of what’s going on, and your videos are absolutely amazing for understanding the actual application and computations, Thank for this excellent content!

[adamjahani]

I was taught a totally different method for the change of coordinates and it didn't make sense. Now it does. Thank you.

[aprildeath]

Thank you so much for making this. You explained it brilliantly man, I truly appreciate it, since I didn´t know how to do these particular types of exercises.

[andyhype]

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[keotshepilemandona]

During this covid 19 is very difficult to learn remotely more especially in our institution, our lecture will send us 7 minutes videos and then questions, I would get confused for days and what’s worse some material from googles and other videos would make things worse, I’m glad that today was my day to come across this videos, stay blessesd.

[lovelylife]

Tomorrow is my exam....but I never get this much clarification in change of basis before this....Happy to find this video

[andrewpalacio]

midterm tomorrow, saving my life. thank you very much.

[tomscott]

this is the best presentation i've seen on basis xformations. i'm tutoring someone and was looking for something clear like this.

[AliRaza-xfir]

Assalam o alaikum. Hope u r fine, got this video very helpful in my concept construction. Thanks

[ML-uuik]

Thank you, sir! I was in desperate need of this, and I so appreciate you posting these.

[Bedoroski]

This saved a lot of my brain power. Thank you

[BgBoyPants]

Thank you! Wasn’t explained or even mentioned by the professor or in the book. Yet somehow we’re expected to know this off the top of our heads by the time the next exam comes around 😒
I really love this stuff though! It makes so much sense now. You did a great job explaining it!

[wryltxw]

not sure why other authors don't introduce the extra notations you provided with the subscripts to clarify the exact meaning. your instructions was much more clearer.

[HassanJMandour]

I noticed that rref[ A | B ] = [ I | P(B to A) ], and I was about to cry :"D

[ruddha]

Thank you so much. This finally made sense.

[myousefzadeh]

Dear Mr. Panagos,
I would appreciate if you let me know the name of software or program you used in your lectures. By that I mean, not video and audio parts of the lecture. Since I’m taking math notes from You Tube lectures, in my PC. I need a tool(s) either software or program which enables me to write math symbols, text and drawing geometric figures, this is what I’m looking for. Any suggestion you might have in this regard would be appreciated. Thanks, fantastic video lecture.

[kkmf-squirrel]

For the augmented matrix, could I just add the other two vectors as columns in order to solve for the entire matrix quickly?