Rudhreswaran G posted an Question
July 16, 2021 • 17:30 pm 30 points
  • IIT JAM
  • Mathematics (MA)

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

1 Answer(s) Answer Now
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  • 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)

  • 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

    cropped1399945322457152474.jpg
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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

  • 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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