Math Help

[Lamplighter]

Professor Strang's best of the day:

Can you sort of think about 9 vectors in 9 dimensional space and take their combinations ?
That's really the central thought that you get kind of used to in linear algebra.
Even though you can't really visualize it, you sort of think you can after a while.

Where was he last month when I had 8 dimensional planes in a 9 dimensional space, and
didn't realize the 9th column was the same as the 8th column and so it didn't add anything new ?