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# Alternate basis transformation matrix example

Example of finding the transformation matrix for an alternate basis. Created by Sal Khan.

## Want to join the conversation?

• hey sal, great vid, but can we get some practice problems? please
• he doent even read these comments i believe. But Hey, I agree
• where can i find practice questions for this?
thanks
• In this video I'm feel confuse about use the same vector for B(basic matrix) and for C(matrix)
• i need to find the representing matrix of the transformation according these basis...how i do that?
B ={(1,0,0), (0,1,1), (2,1,0)} E ={(1,0,0), (0,1,0), (0,0,1)}
T : R3 ->R3
T(x, y, z) = (x - 2y, y + 2z, x - 2z)
• first, you need to transform all the vectors of the INPUT basis, [(100)(011)(210)]. That should give you these vectors: (101)(-23-2)(011) -I could be mistaken..- Then, since your OUTPUT basis is the standard one, you just create a matrix in which the columns are the transformed vectors' coordinates in the output basis (like I said, since you have the standard basis the coordinates for any vector in relation to that is the vectors coefficients themselves. In this case, the columns for your transformation matrix are just that, so you should get:

1 0 1
-2 3 -2
0 1 1
• Hi I need to determine f(x,y)=?; I have [f]B B'=(2 -1
0 1) where B={(1,1),(1,2)} and B'={(1,0),(0,1)} can please someone show me how to do that? thans
• question isn't written clearly enough to be understandable
• If there is two different basis M N for R3, its basis matix is A and B(both invertible). So A[x]m=B[x]n=x, which also means B^(-1)A[x]m=[x]n. Are the column vecors of B^(-1)A the same as the column vectors in A if we think they are respect to B coordinate? If they are, our take away can be extended to a general form. Exciting!
• standard basis of deivative map
• Does the order of the vector matter in the basis matrix? I mean, can I use either [(1, 2)(2, 1)] or [(2, 1)(1, 2)]?