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I have some questions about vector spaces, I would really apreciate if somone could read this and let me know if I understand things or not, and if not let me know where I have it wrong.

I am having a lot of trouble UNDERSTANDING how to find the intersection of two vector spaced and how to find the space of solutions of a system of equations.

Given two spaces and there bases as vectors I think the way to find the intersection is to write a matrix with each vector as a column. This is because I am looking for a linear combination of these vectors that equals 0. Since if it equals 0 then there is an equivalence between the vectors.

Having taken this matrix and brining it to reduced row echelon form, what do I do from here? More importantly, do I understand this coorectly?

With a system of solutions: Given a number of equations I would put each equation in the matrix as a row and bring it to reuced row echelon form. This is because in this case I am searching for the dependencies between variables in the equations by combining them. So if I have a single 1 in each row and everything else zero than that variable is equal to the coresponding entry in the solutions column.

If there is a row with two variables then the opening variable (the first entry in that row with a 1) is tied to the other variable.

I just need to know if I understand this or not as when I try to solve problems I am unsure of myself because I am not sure if i know what I am doing or not.

Thanks

Tal

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: General questions about intersection of subspaces

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