Linear Alg: Rowspace Solution to Ax=b example

[mcwhitfield09]

I've been picturing a line and plane in R3 in my head to get me through the last 3 or 4 videos. Thanks for finally getting to this and confirming my intuition :)

[LaureanoLuna]

There are a couple of things I'm not clear about.

How can the 'shortest' solution to Ax=b be nonzero and lie in the rowspace of A if the solution set of that equation is orthogonal to that rowspace (see 12.42)?

Second,it seems to me that the notion of vector addition has been changed: [0 3] + c[2 3] is no longer the diagonal of the corresponding parallelogram but c[2 3] displaced by [0 3]. I'm confused about a line representing the vectors in it or the vectors that point to it.

[V2PRC]

This video is duplicated in the playlist of Linear Algebra.

[deathbystarship]

oh my god sal how the hell did you make all of these... you are a god.

[norwayte]

Good. Thank you.

[Waranle]

Thank you Sal :)