"Is it the same to write the answer of basis in row or column?"


There is some disagreement between authors on how strict to be with row vs. column vectors. I will provide you with the answer to my opinion and therefore how this course is taught.

 

In a lot of contexts it does not matter whether you write any given vector as a row or column vector. For example a vector in R^n could be written as,

 

x = (x_1, x_2, ... , x_n)

or,

 

x= x_1

     x_2

      

     x_n

 

The information is exactly the same and comes from the same vector space.

 

Therefore when I give the basis of a vector space I tend to (but not always) write them as rows just to save space on the paper. It is a matter of style.

 

However...

 

There are some contexts for which it is wrong to write a row vector instead of a column vector. Generally this is when there is some kind of matrix multiplication going on because the dimensions must match.

 

So in summary, for this course you may write isolated vectors in either row or column format, but when there is special context that requires matched dimensions (such as matrix multiplication) then you must write the appropriate one.