# Homework Help: Vector spaces: column spaces

1. Mar 5, 2008

### Benzoate

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

For each of the following choices of A and b, determine if b is the column space of A and state whether the system Ax=b is consistent

A is a 2 by 2 matrix , or A=(1,2,2,4) , 1 and 2 being on the first row and 2 and 4 on the second row. and b=[4,8] 4 being on the first row and 8 being on the second row . Ax=b
2. Relevant equations

3. The attempt at a solution

I know the system is consistent , because the system has infinitely many solutions. I haven't the first clue of how to determine if b is in the column space of A .

Last edited: Mar 5, 2008
2. Mar 5, 2008

### Mathdope

Can b be expressed as a linear combination of the columns of A? If the system is consistent, well...

Last edited: Mar 5, 2008