Dimension of column- and rowspace

[Niles]

[SOLVED] Dimension of column- and rowspace

Homework Statement

My book doesn't answer this question clearly, but I have notived the following connection:

Does the dimension of the rowspace of a matrix equal the dimension of the columnspace of a matrix which equals the rank of the matrix?

 

[ColdFusion85]

If the matrix has real elements, the row and column spaces have the same dimension. Furthermore, the rank of A equals the dimension of the row space of A.