Understanding Scalar Transformations in Matrix Dimensions

[the_kid]

Just a quick question I've been giving some thought to today. Suppose A is an mxn matrix with column vectors such that only one of them is a scalar transformation of another. What can we say about the relationship of m and n?

 

[the_kid]

No thoughts?

 

[mathwonk]

what is a "scalar transformation"? if it means scalar multiple, then i don't see right off how to say anything. if it means linear combination, in the sense that there are n-1 independent columns, then it say the column rank is n-1. since then the row rank must also be n-1, we know there are at least n-1 rows, so m ≥ n-1.

your problem in receiving no answers is your unclear statement of the question.