Matrix Spaces

MIT 18.06SC Linear Algebra, Fall 2011
Instructor: Ana Rita Pires

A teaching assistant works through a problem on matrix spaces.

License: Creative Commons BY-NC-SA

[sergiohuaman]

I suffered with this one. Nice! It means I'm still to learn and interiorize more this material.

[ath]

I've got a question,
1. why don't we also assume that c = 0 and multiply this by the sup-set of matrices that have the vector [2 1]' in it's column space? just the same way we did to the first sup-set which turned out to be a sup-space (because we assumed c = 0)?
Thanks alot.

[cheekyiscool]

I am trying to figure out if there is another method to find the basis? For example, use reduced form of a matrix, identify free variables, and derive vectors that form the basis?

[TheLevano]

why did we automatically assume that the result will be [0, 0]?

[benthomson]

maybe the question should mean "matrix subspace"

[AndrewJames]

What is to stop us from separating [a b -2a-b] into a linear combination of [a 0 0], [0 b 0] and [0 0 -2a-b] instead of [a 0 -2a] and [0 b -b]?

Is it because we have a 2x3 matrix and thus the rank of it must be less than or equal to 2 and so we can only have 2 linearly independent basis vectors?

[nakamura]

why the dimension of the subspace is 4? You can have multiple combinations

[lin]

May someone explain the step at 06:14 from the vectors [a, 0, -2a] + [0, b, -b] to [, 1 0, -2], [0, 1, -1]. I clearly see that the second vectors are derived from the first pair, but I dont get why each row must satisfy this and how this implies the last step to the basis... :/
Thanks in advance :)

[gilgameshgawande]

Really good explanation...I like ur smile!