# Using Dimension Formula of a Matrix

1. Oct 15, 2011

### tatianaiistb

1. The problem statement, all variables and given/known data
If VΩW contains only the zero vector, then dim(V+W)+dim(VΩW) = dim(v) + dim(W) becomes dim(V+W) = dim(v) + dim(W). Check this when V is the row space of A, W is the nullspace of A, and the matrix A is mxn of rank r. What are the dimensions?

2. Relevant equations

dim(V+W)+dim(VΩW) = dim(v) + dim(W)

3. The attempt at a solution

I don't even know how to start this problem.

I do know that dim(V+W) + dim (VΩW) = rank of [A B] + nullity of [A B]

Can anyone help??? Thanks!
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Oct 16, 2011

### HallsofIvy

Staff Emeritus
It would help if you told us what thes symbols mean. I presume that V and W are vectors but what is $\Omega$ and what do you mean by $V\Omega W$?

3. Oct 16, 2011

### tatianaiistb

I'm sorry! That symbol means V intersects W... And yes, V and W are vectors.

4. Oct 16, 2011

### Staff: Mentor

No, V and W are vector spaces.