# Understanding the concept of vector

1. Oct 23, 2005

Hi ,
I have hard time understanding the concept of vector, matriecs in relation with rank and independent/dependent columns / rows.
I have two question that I would like to have help:
The set of vectors {v1,v2,v3,v4} would be linearly dependent if
1-v3 is the zero vector
2- each of the vectors is in R3
3- the row reduced form of the matrix whose columns are the given vectors has rank less than 4
4-the row reduced form of the matrix whose rows are the given vectors has rank less than 4
5- any of the above would imply dependence

I would chose 3 or 4:
Please can you help me to define the expressions "the row reduced form of the matrix whose columns are the given vectors"
Is that means that the matrix would be like
[a b c d]
[e f g h]
[i j k l ]
where a,e,i are the coordinates of v1
b,f,j are components of v2
c,g,k are components of v3
d,h,l are components of v4?
Thank you very much
B.

2. Oct 24, 2005

### HallsofIvy

Staff Emeritus
That is the "matrix whose columns are the given vectors", now you would need to row-reduce it.

3. Oct 24, 2005