Deriving a method for determining inverses | Matrix transformations | Linear Algebra | Khan Academy

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Determining a method for constructing inverse transformation matrices
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Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.
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[@Postermaestro]

This is just pure gold. Understanding how linear algebra works, makes it 10000 times more satisfying to solve problems with matrices, as opposed to just learning how to use it.

[@Phi1618033]

75 excruciating videos later, WE HAVE ARRIVED!

[@norwayte]

THAT is good. I've never seen it that way - step by step to inverse. You are really the master of explaining things. Thank you.

[@droo3640]

When I first watched this I was confused for a moment about the whole idea of row operations being equivalent to transforming the column vectors. So I figured I'd post here just to clarify for anyone else who found that confusing. One way to understand it is to visualize how different row operations affect each column - some example row operations (R1 = row 1, etc.):
R2 = R1 + R2 - This is equivalent to changing the second item in each column of the matrix to the sum of itself and the element directly above it
R3 = 3R3 - This is equivalent to just multiplying the third item in each column by 3
So even though you're doing "row operations", you can think of it as doing it to each column one at a time.

[@aydansmith6145]

Amazing video, not enough educators go as in depth conceptually as you do.

[@yiliangliang5694]

Bravo. This is clearer than anything written on the textbooks.

[@matthewsarsam8920]

Man this helped a lot

[@alkalait]

i hope in later videos you also mention about cases where row permutations are needed in case a pivot is not where it's supposed to be

[@DukeLe35]

give this man a medal!!!
you made linear algebra sexy indeed!!!

[@Postermaestro]

2:39 For anyone wondering what's happening here, he is using the fact that S · I = S. It confused me for a while.

[@Aesieda]

Thanks.

[@BudskiiHD]

Amazing!!

[@steveg12345678910]

Smoke weed my bredrins!