# Thread: when do you

1. ## when do you

When do you write the vector in a row or column... our book/ teacher seems to jump back and forth...

2. Originally Posted by mpl06c
When do you write the vector in a row or column... our book/ teacher seems to jump back and forth...

It is pretty arbitrary but sometimes it is VERY important which one's used. For example, a row vector with n components can been seen as a 1 x n matrix, and the same column vector as a n x 1 matrix ==> you can matrix multiply the former by the latter (in this exact order!), but NOT the other way around unless n = 1.
Don't worry, you'll see this later on.

Tonio

3. ok now if ur finding the determininit does it matter which way?

4. ok now if ur finding the determininit does it matter which way?
Note that determinants are only associated to square matrixes. The determinant of
a vector (row or column) is undefined.

5. right...so for a 3x3 matrix... will the determinant be the same if you write the vectors in columns or in rows.. will they be the same

6. Originally Posted by mpl06c
right...so for a 3x3 matrix... will the determinant be the same if you write the vectors in columns or in rows.. will they be the same

This is an oddly worded question: do you mean to ask whether the determinant of a matrix is the same if we write rows as columns and the other way around? If so the answer is yes, because the deter. of a square matrix equals the deter. of its transpose (google it).

Tonio

7. ok thanks... one last question...

why in calculus is the vectors written in like <1,3,5>

and in my book it would be written as
[1
3
5]

??

8. Originally Posted by mpl06c
ok thanks... one last question...

why in calculus is the vectors written in like <1,3,5>

and in my book it would be written as
[1
3
5]

??

If yours is a book on linear algebra then there you'll use much more column vectors than row ones.

Tonio

9. thanks.. so would i be correct in saying that for solving systems of equations one would set the vectors in row form

and for spans, determinants, subspaces etc.. the vector in rows....

10. When you say solve systems of equations you mean Gauss or
Gauss-Jordan reduction, right?

Then you operate on rows, and your aim is to set the system in row-echelon form.
You could although in theory write everything as columns, but it would be
awkward to write an equation like "x+y=4" on it's side.

Now for spans and general vectors it doesn't really matter which way you write it.
The reason you write spans usually with column vectors is that they look
nicer side by side than row vectors (and you will see another reason when working with
linear maps as matrixes) . It is just convention to write it
as column vectors.

Like tonio said before the determinant of a matrix is independant of wether
you write the vectors as columns or vectors.

Your calculus book probarbly writes vectors like rows because you are
used to working with cordinates (x,y) before.

So my point is it really doesn't matter, don't waste too much time thinking about
whether to write rows- or columns . Try to focus on other more important things in
your linear-algebra class.
Hjörtur

11. thanks u everyone ... appreciate it alot!