Confused about Column Space? Let Us Help!

[kolycholy]

so i tried looking it up on various sources including wikipedia, and i am still confused about column space actually is.
maybe it would help if one of you explained it to me?

 

[FunkyDwarf]

basically with the row space you have a subspace spanned by the rows (did this unit last semester so kinda hazy :S) with the column space its the same thing but you have to convert the matrix into a useable form. So if you have

[a b]
[c d] then to get the rows you need for the column space you flip it to get
[a c]
[b d]

you then do the same row operations as you would for a row space
hope this helps (and is right :P)

 

[HallsofIvy]

The "column space" of an nxn matrix is the subspace of Rⁿ spanned by the individual columns of the matrix, thought of as n vectors.