Exploring the solution set of Ax = b | Matrix transformations | Linear Algebra | Khan Academy

Exploring the solution set of Ax=b (non homogeneous equations)

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[Polyphemooos]

I just wanna say a big thanks to you, Sal. I've been watching this linear algebra playlist for over 10 hours ( I got that sun badge! ). Before these video's I hate this course but now I actually like it because I understand it. Really a big thanks to you! You are helping mankind in general :)

[rfmvoers]

14:50 would it really be the "union"? To get the solution space of Ax=b we add xp to any vector xh from the null space (shifting the null space by xp), but that's not the same as the union of xp and the null space, is it? I believe "union" suggests that the null space itself would be part of the solution space of Ax=b, which is not true.

[nonesta]

is there a video with a 3x3 for A vector matrix and an 2x1 b vector with actual numbers in it?

[histand]

You're always so good at explaining this in a down-to-earth sort of way. Thank you

[alexshei]

could you please tell me the book which you are using to teach linear algebra? thank you very much!

[BestFanEver]

this is the one thing that helps in math

[zhilinglin]

I really can't get it when Sal said the Solution Set is some particular vector Xp Union with N(A) at about 15". I thought he just showed by the example the solution set is Xp + N(A). It is '+' instead of Union. These are different, aren't they?

[junecnol]

matrix A dot products with vector xp is [5, -5] which is vector b
i took long time to understand this.

[akeemlouigarde]

Khan academy you're making everything sound very complicated, we just want to use the technique. However, thank you for your help.

[paxylly]

The null space aha moment was magical.

[Sheeeeshack]

Can somebody plz tell me what Homogenous and non-homogenous equation is……

[danbailey]

This video requires some prerequisite knowledge. First a good understanding of functions of a single variable with the terms domain, codomain, and image. It also requires an understanding of Matrix multiplication. Then and only then will you understand that a 2x2 matrix is multiplied by a vertical pair of numbers and produces a 2nd vertical pair of numbers. The first pair of numbers is an element from the domain(input) the second pair of numbers is the image of the first pair(output). That's just to get started. This is not algebra I.

[cryptonative]

@EXT109 there are 72 videos before this you should watch them all of them to understand