Linear Algebra Example Problems - Change of Coordinates Matrix #1

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.

[scntutor]

Thank you so much is best to have u as a mentor

[albertmendoza]

I feel like John C. Reilly is teaching me some linear algebra.

[maxpercer]

Your notation is the simplest to understand.

[esa]

Usually these questions would have you convert a polynomial set into a set in R^n via coordinate mapping.

[kkmf-squirrel]

So by your rationale, if you need a transition matrix to convert coordinates in the B basis to the standard basis, it will essentially be the vector matrix of the basis B?

[nisamiyim]

At 6:17, weren't the vectors in the standard basis and the B basis the opposite?

[pde]

Sir if we take a subspace of dim 2 of R3. Then the change of coordinate matrix is of order 2 then how a vector can be change it's coordinate by multiplication of change of coordinate matrix?

[allipraveenkumar]

Half of your screen is covered by the subtitles.even though I can understand ur voice clearly I don't know why u r giving the subtitles..this makes me hard to see the full screen, as I can able to see top part only.remove that and then it will be much good.❤️