# Linear Algebra: dimension of subspace question

## Homework Statement

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

## Homework Equations

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

## 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?

## Answers and Replies

Dick
Science Advisor
Homework Helper
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.

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

Dick
Science Advisor
Homework Helper
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.