Linear Algebra 8k: You and I Have a Problem - We Need Some Distance!

[afendin]

Didn't know why do we need inner product in its pure and abstract form until I watched this video. Спасибо вам огромное!

These lessons are pure gold. If you look closely, at 2:00 it's possible to see "least squares" up his sleeves. 😂

[RUMI]

I am a little confused about, what would be the column space of this system.
Is it,
a
{[b]}
4a+5b
7a+11b ?

And because it has two independent variables or two degrees of freedom (a & b), the dimension of the column space is 2. Even though the actual column vectors are themselves 4-D.

Am I correct about the above statements?