# Linear Algebra: dimension of subspace question

1. Jun 30, 2009

### jack_bauer

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

Find an example of subspaces W1 and W2 in R^3 with dimensions m and n, where m>n>0, such that dim(intersection of W1 and W2)= n

2. Relevant equations

dim(W1+W2)= dim(W1) + dim(W2)-dim(intersection of W1 and W2)

3. The attempt at a solution

Well what I know for sure is that I have to use the equation dim(W1+W2)= dim(W1) + dim(W2)-dim(intersection of W1 and W2). I'm just really confused on how the subspaces should be. Should they maybe be matrices?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Jun 30, 2009

### Dick

Subspaces are spans of sets of vectors. If you are working in R^3 then your only choice to make m>n>0 is m=2 and n=1, right? Pick the standard basis, e1=(1,0,0), e2=(0,1,0), e3=(0,0,1). One subspace with dimension 2 is span(e1,e2). A subspace with dimension 1 is span(e1). Do you have any idea what I'm talking about?? Do you know what a span is? Your question about whether the answer is a matrix makes me think we should start from the basics.

3. Jun 30, 2009

### jack_bauer

lol, yeah I know what you are talking about. I'm just really lost with this stuff right now. thanks man.

4. Jun 30, 2009

### Dick

The way to get unlost is to try to solve it. Give me two subspaces, tell me their dimensions, tell me the dimension of their intersection, tell me the dimension of their sum, etc. Show me the formula works. ANY two. They don't even have to solve the problem. You don't even have to be right. Just DO something.