Linear Algebra Example Problems - Finding 'A' of a Linear Transformation #2

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A linear transformation can always be represented as a matrix operation on some vector x. In this example we're told values for T(e1), T(e2), and T(e3) where ei are "coordinate vectors". These vectors have a zero in every coordinate except a single one in their "ith" coordinate. Using this information we construct the standard matrix representation of the linear transformation T. We also use the linearity property of the transform to find T(x) for another vector x.

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Thank god I found this channel. Easier to understand than my professor :)

abhishekchaudhary

Had a really hard time with this concept in particular, this finally helped me understand. Thank you

waterman

Adam Panagos, Great video and content. Loved the step by step writing approach. Thanks for uploading!

MechanicalEI

You explain it so perfectly until you skip that step i should know 🤷‍♂️ 😀

GustavoSilva-srpi

thank you sir this is very useful and clear

manellallem

Sir, if I write e1=[2, -4, 1] then matrix A would not transform e1 to T(e1). In given example e1, what has been taken as a basis vector, is transformed by A, what you have constructed, to T(e1). here a21, a31 of e1 is zero consequently A.e1 becomes T(e1). please let me know if I take mine, given above, e1, how it will be transformed by same A, or I have to construct another A.

Monkavenger

At 4.10, it is not coming out to be same T(e1) = Ae1 ...not coming same both side

amirahmed

hello, can u let me know how to find T(e1), if A is given?

tahelanipankaj

i have a problemm:/ i have to find the standard transformation T(x, y, z) and im told that ker(T)=<{(1, 1, 1), (1, 0, 1)}> and T(1, 2, 3)=(1, -1)
btw the transformation goes T:R3->R2 help please

gonzalorojas

Did you choose (e1), (e2), (e3) for the last problem. I understand that you can pull out constants in the linear transformations, but I don't see where (e1, e2, e3) come from?

abrahammaldonado

i thought a transformation from a dimension to a higher dimension is impossible. from 3d to 4d, as it is in this case

bsp

I didn´t understand the step at 6:29 either...

ylvaeriksson

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