I had one doubt in matrix form of linear equationsSay , 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(A∣b)=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(A∣b)=n and can't ever be n+1.

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I had one doubt in matrix form of linear equationsSay , 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(A∣b)=n or can we say that since b is a linear combination of the component vectors in A then augmenting it in A won&#039;t increase the number of linearly independent column vectors and hence the rank(A∣b)=n and can&#039;t ever be n+1.

zahrkao8vm · Accepted Answer

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

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

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