how to calculate rank of 2 by 1 matrix..??

shivaniits

hey guys so i am well familiar with finding out rank of square matrices but if matrix is just a row or column vector then how to determine its rank..considering the example below:
a=[x1
x2
x3]
where is column matrix while x1,x2,x3 are elements of this matrix..!!

mfb

Can you find the column rank (the number of independent columns)?
This is the same as the rank of the matrix.

shivaniits

hi there
infact i am quite asking about how to calculate the rank of a column or row matrix..??
and here i have just taken the example of row matrix..but i would also like to know about determining rank of a column matrix..!!

HallsofIvy

Any "n by 1" or "1 by n" matrix has rank "n".

mfb

And I posted a hint.

It has rank 1, if at least one entry is non-zero, and 0 otherwise. But never n, unless n=1.

shivaniits

ok..but here you have mentioned about column rank...but i am asking here is a different thing..i am asking about how to find the rank of column matrix or column vector i should say..!!

mfb

It is not a different thing.
Can you find the column rank of a column matrix? It is easy, and the answer was already posted here. The same applies to a row matrix and the row rank.

shivaniits

ok so can i say that any n by 1 or 1 by n matrix has rank of 1 ..!!
but what if the independent rows or row vectors and columns or column vectors have value more than 1 like i have an example as:-
x1=(1,3,4,2)
x2=(3,-5,2,2)
x3=(2,-1,3,2)
so here i have three vetors x1,x2,x3 out of which two are independent x1,x2 while x3 is dependent as x3=(x1+x2)/2;
and they all form a column matrix of 3 by 1 as
A=[ x1
x2
x3 ]
now acc to rule n by 1 and 1 by n we have rank 1 but checking independent rows as 2
so what should be rank 1 or 2..??

mfb

2. I don't see any reason why you would expect 1. It is a 3x4-matrix, this is neither nx1 nor 1xn.

shivaniits

now i am feeling stupid..!! i have been looking all along in terms of an individual vectors and not in terms of components ..!!
thanks..:)