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

Determining a method for constructing inverse transformation matrices

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[Phi]

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.

[yiliangliang]

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

[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

[aydansmith]

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

[droo]

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.

[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.

[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.

[DukeLe]

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