Change of coordinates

Computing the change of coordinates matrix from a basis B to a basis C and using this to calculate new coordinates given old coordinates.

[drpeyam]

Note: At the end, it should be:

-3 1
-5 2

And the answer is

-5
-8

[maxpercer]

I like how you went through the 'slow way' first, which sets up the motivation for the transition matrix (and also helps define it), instead of just presenting the transition matrix unmotivated.

[jiyoonpark]

Every time I search youtube for a linear algebra video: “I hope Dr Peyam covered this topic..”

[Rundas]

The grade I got for my linear algebra 1 exam was not enough, so I hope that you will cover as much as possible that I can take this exam once more with a better understanding of the topics.
You are just better at explaining than my professor or their scientific assistants.
:D

[Behroozifyable]

Yes I would say the same. The rref gives
- 3. 1
-5. 2
And the x goes to - 5, - 8 but otherwise a fantastic video!

[Debg]

I have just got a new mobile device and I am testing its resolution with your video. Math never looked so neat!

[maxpercer]

I just had one question, you defined the change of basis matrix P_ {C<--- B}, but you never defined P_B, without the arrow. Is that still a change of coordinate matrix? It looks like you understood P_B to be the matrix of basis vectors of B in column form.

[sugarfrosted]

This is cute, you're essential doing a change of basis to the standard basis to get the transformation matrix.

[aneeshsrinivas]

Dr peyam ive been wondering something about coordinate vectors with respect to a basis denoted the way it is.Why is the coordinates of [X] with respect to B denoted X_B shouldnt it be X^B so that the identity [Id]_B^C[X]^B makes more sense as the superscript and subscripts cancel just like how

[T]_Y^Z*[U]_X^Y=[TU]_X^Z. They messed up on the notation here.

[ssdd]

12:34 shouldn't the top right be |-3 1]?