realtion between columns and rows of a matrix and space

[HelpNeeder]

Suppose A is an mxn matrix.
The columns of A span R^m. Why is it R^m and not Rⁿ?

 

[lex]

When you multiply a column vector containing n elements, by a matrix with m rows (and n columns) you get a column vector with m rows.
Remember when you multiply Ax you are getting a linear combination of the columns of matrix A (each of which contains m elements).

 

[HelpNeeder]

Thank you. I understand it now.

 

[Steven G]

No one can answer your question since you never gave the size of matrix A. Do you see that? Having said that, Lex gave a good response.

 

[lex]

@Jomo

No one can answer your question since you never gave the size of matrix A. Do you see that? Having said that, Lex gave a good response.

Suppose A is an mxn matrix.