I had one doubt in matrix form of linear equations Say , we have a system of equations Ax=b

ymhonnolfq

ymhonnolfq

Answered question

2022-02-23

I had one doubt in matrix form of linear equations
Say , we have a system of equations Ax=b such that A is an n×n matrix and b is a n×1 matrix and so is x then, if we are told that rank(A)=n, then, do we need to check that rank(Ab)=n or can we say that since b is a linear combination of the component vectors in A then augmenting it in A won't increase the number of linearly independent column vectors and hence the rank(Ab)=n and can't ever be n+1.

Answer & Explanation

zahrkao8vm

zahrkao8vm

Beginner2022-02-24Added 10 answers

I am not sure that I understand you when you write “do we need to check”. Assuming that rank(A)=n, then rank(Ab)=n if and only if the system Ax=b has a solution. Does this answer your question?

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