Compositions of linear transformations 2 | Matrix transformations | Linear Algebra | Khan Academy

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Providing the motivation for definition of matrix products
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[@blackphoenix1207]

Thank you for all of the linear Algebra videos!!!!!

[@Estinox]

Thanks so much Sal!!! This video directly correlates to what my assignments are on. Tytyty!

[@jonathanjordan21]

7:47
Typo detected!
Matrix A order is m x n

[@junecnol79]

thanks for excellent tutorials. 13:28 i think it should be "Rm" not "Rn"

[@jaywu4956]

yes that's correct

[@TazGGGUNOT]

Thanks a lot for your effort Sal. Greetings from Sweden!

[@uisucho5881]

14:52 헷갈렸던것

[@geekionizado]

Where did you find this??? Wow :)

[@DerMigi]

I love you man

[@alirezagholami1946]

excellent

[@yustinayasin5539]

12:46 why he multiple B(Ax) with x vector again?

[@jonathanjordan21]

the first multiplication by Identity Matrix was for the entire span of R^n which basis are the Identity Vectors.
Naturally, Matrix A(m x n) times Identity Matrix(n x n) is Matrix A(m x n)
The video just put the vectors of matrix A (columns of matrix A) onto the columns of matrix C with a multiplication of matrix B on each column.
again, Matrix multiplication of a vector is a linear transformation. That means matrix B transforms each vector of matrix A and then matrix A transforms the vector x.
Matrix multiplication is associative, it doesn't matter which one gets multiplicated first