- Thread starter diogomgf
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what does this mean?and \(\displaystyle B\) is a matrix based on any column of \(\displaystyle A\).

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That \(\displaystyle B \in M_{m \times 1}\), where \(\displaystyle B\) is a random column of \(\displaystyle A\). It is supposed to be irrelevant...what does this mean?

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In all cases?Because B is not included in calculating r (A|B)

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I will let you decide. Was there anything special about your A and B or were they just arbitrary matrices?In all cases?

By the way, how do you determine the rank of a matrix? How about the rank of a system of equations?

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Well my O.P was to understand why in this specific scenario B doesn't influence the outcome of the rank of the system of equations.I will let you decide. Was there anything special about your A and B or were they just arbitrary matrices?

By the way, how do you determine the rank of a matrix? How about the rank of a system of equations?

To determine the rank you just transform the matrix A (as in [A|B]) to row echelon form and see the number of non-null rows obtained.

The same can be said about the augmented matrix. Sometimes the matrix B obtained does influence the rank of the matrices (I asked "in all cases?" but I shouldn't have )...

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Thats what I'm trying to knowHow does the matrix B obtained does influence the rank of the matrices?

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How do you determine the rank of a matrix? How do you determine the rank of a system of equations? You answered those--thank you.Thats what I'm trying to know

Now I have a different question. What is the differences, if any between the two methods?

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There isn't any difference. You just have to put the system of equations as an augmented matrix and find the rank...How do you determine the rank of a matrix? How do you determine the rank of a system of equations? You answered those--thank you.

Now I have a different question. What is the differences, if any between the two methods?

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So use that as your justification as why the two ranks are equal?There isn't any difference. You just have to put the system of equations as an augmented matrix and find the rank...

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I don't understand that question.So use that as your justification as why the two ranks are equal?

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Got it ! Thank youSo use that as your justification as why the two ranks are equal?