How to calculate rank of 2 by 1 matrix?

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    Matrix rank
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Discussion Overview

The discussion revolves around how to calculate the rank of a 2 by 1 matrix, specifically focusing on both column and row matrices. Participants explore the definitions and conditions under which the rank is determined, including examples and specific cases.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant asks how to calculate the rank of a 2 by 1 matrix, expressing familiarity with square matrices but uncertainty about vectors.
  • Another participant suggests that the column rank, which is the number of independent columns, is the same as the rank of the matrix.
  • A participant seeks clarification on calculating the rank for both row and column matrices, indicating a desire for a comprehensive understanding.
  • It is proposed that any "n by 1" or "1 by n" matrix has rank "n," but further clarification is provided that it has rank 1 if at least one entry is non-zero, and 0 otherwise.
  • One participant questions the application of the rank definition to a specific example involving multiple vectors, leading to confusion about whether the rank should be 1 or 2 based on independent vectors.
  • Another participant points out that the example given is a 3x4 matrix, which does not fit the "n by 1" or "1 by n" definitions.
  • A participant expresses realization of a misunderstanding regarding the consideration of individual vectors versus their components.

Areas of Agreement / Disagreement

Participants express differing views on the rank of matrices, particularly when considering independent vectors versus the definitions of rank for specific matrix dimensions. The discussion remains unresolved regarding the rank of the example provided.

Contextual Notes

There is a lack of consensus on the application of rank definitions to specific examples, and some assumptions about the independence of vectors are not fully explored.

shivaniits
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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..!
 
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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.
 
  • #10


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

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