# How to calculate rank of 2 by 1 matrix?

• shivaniits
In summary, the rank of a 2 by 1 matrix can be determined by the number of independent columns, which is also the same as the rank of the matrix. For a column matrix, the rank is equal to the number of entries in the column, unless there is at least one non-zero entry. In the case of a row matrix, the rank is always 1. However, if there are multiple rows or columns with more than one entry, the rank can be determined by the number of independent rows or columns. In the example provided, the rank of the given matrix is 2.
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..!

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

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..!

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

shivaniits said:
infact i am quite asking about how to calculate the rank of a column or row matrix..??
And I posted a hint.

HallsofIvy said:
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.

mfb said:
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..!

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.

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..??

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

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

## What is a rank of a matrix?

The rank of a matrix is the maximum number of linearly independent rows or columns in the matrix. It represents the number of essential dimensions in the data contained in the matrix.

## How do you calculate the rank of a 2 by 1 matrix?

The rank of a 2 by 1 matrix can be calculated by checking if the two rows or columns are linearly independent. If they are, then the rank is 2. If they are not, then the rank is 1.

## What is the difference between a 2 by 1 matrix and a 1 by 2 matrix?

A 2 by 1 matrix has 2 rows and 1 column, while a 1 by 2 matrix has 1 row and 2 columns. The order of the elements in a matrix can affect its rank, so the rank of a 2 by 1 matrix and a 1 by 2 matrix may not necessarily be the same.

## Why is it important to calculate the rank of a matrix?

The rank of a matrix can provide important information about the data contained within it. It can help determine the dimension of the data, identify linearly dependent or independent variables, and aid in solving systems of linear equations.

## Can the rank of a matrix be greater than the number of rows or columns?

No, the rank of a matrix cannot be greater than the number of rows or columns. The rank is limited by the number of linearly independent rows or columns in the matrix, which cannot exceed the number of rows or columns.

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