How to calculate rank of 2 by 1 matrix?

[shivaniits]

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

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]

infact i am quite asking about how to calculate the rank of a column or row matrix..??

And I posted a hint.

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

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

 

[shivaniits]

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

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..:)