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###### 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 Best Answer

hope you get what you wanted to know.

• ##### Ankur Rao

still have doubts

no if I have I will ask 👍

okk

if you find solution useful then you can select it best answer

• ##### Ankur Rao

any other doubts.

so we want to consider B as constant

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

rank is 2 here and column is also 2

it is three know?

okk you took it wrong columns before= sign

in [A:B] column of A only

feel free to ask if you have any doubts

only we want to take columns of A only no need to take A:B

yes

ok

so B is consider as constant

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

that's ok but in book they have given that explanation so that is confusing

it is explained in different way when we don't have a square matrix

ok

any other doubts

no

we want to take A only as columns

check out this

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

now it depend on (n-r) if the solution are unique or infinite and that different conditions is given in your uploaded text

read these last two comments together

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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