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Rudhreswaran G posted an Question

July 16, 2021 • 23:00 pm

30 points

IIT JAM
Mathematics (MA)

Can some one explain this ? also tell what is n-r and m-r ?

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A
Ankur Rao Best Answer

hope you get what you wanted to know.
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A
Ankur Rao

still have doubts
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no if I have I will ask 👍
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okk
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if you find solution useful then you can select it best answer
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A
Ankur Rao

any other doubts.
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so we want to consider B as constant
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to have solution unique or infinite the first condition is that rank(A)= rank(A:B)
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R
Rudhreswaran g

but as the information given I have related the problem to that but rank is not equal to columns but how it is unique soluntion
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rank is 2 here and column is also 2
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it is three know?
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okk you took it wrong columns before= sign
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in [A:B] column of A only
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feel free to ask if you have any doubts
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only we want to take columns of A only no need to take A:B
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yes
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ok
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so B is consider as constant
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no the common think which can be said that if rank (A) = rank(A:B) then we will get solution it may be unique or infinite
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that's ok but in book they have given that explanation so that is confusing
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it is explained in different way when we don't have a square matrix
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ok
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any other doubts
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no
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we want to take A only as columns
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check out this
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we will check rank of matrix A and rank of matrix (A:B) , if the rank are equal we will say that system is consistent i.e. system have solution
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now it depend on (n-r) if the solution are unique or infinite and that different conditions is given in your uploaded text
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read these last two comments together
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ok thank you
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A
Ankur Rao

m is row if rank is r then their are r linearly independent rows so we can make (m-r) rows as zero rows by using r rows because (m-r) rows are linearly dependent. So by this we can eliminate (m-r) equations because these are zero rows .
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