Linear Algebra when to write matrix as a col. vector vs a row vector

[bchapa26]

1. My question is a general question that I need the answer to so that I can fully understand the homework I am doing. When do I write given vectors as columns of a matrix, and when do I write them as rows of a matrix? More specifically, how do I write the vectors when finding:

1) Ker(T)
2) Linear Transformations
3) Basis

And rather than memorizing, is there a way to logically understand why I am writing the vectors as such? I'm sorry if this is vague, I am just trying to understand this material better. Thank you!

 

[ArcanaNoir]

For finding the kernel you make the vectors into columns. Not sure about the others.