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mkumar441

  • 2 years ago

please solve this ... suppose A and B are n by n matrices,and AB=I.prove from rank(AB)<=rank(A) that the rank of A is n . So A is invertible and B must be its two-sided inverse. Therefore BA=I(Which is not obvious!).

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  1. mathslover
    • 2 years ago
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    So what we have to do .. ?

  2. mathslover
    • 2 years ago
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    ok sorry wait

  3. mathslover
    • 2 years ago
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    as given that A is n by n, rank(A) \(\le\) n and conversely : n = rank(\(I_n\))=rank(AB)\(\le\)rank(A)

  4. mathslover
    • 2 years ago
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    got my point @mkumar441 ?

  5. mkumar441
    • 2 years ago
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    yes i got it thank you for ur quick response

  6. mathslover
    • 2 years ago
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    Your welcome dear.. also: \[\huge{\mathbb{WE}\textbf{LC}\mathcal{OME}\space\textit{TO OPENSTUDY}}\]

  7. mkumar441
    • 2 years ago
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    i need small favour at wat timings do u present inorder post questions.

  8. mathslover
    • 2 years ago
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    i didn't get you .. it seems that you are Indian. You can ask in Hindi?

  9. mkumar441
    • 2 years ago
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    yes i am indian but i dont Hindi.When do you be in online inorder to clarifiy my doubts?

  10. mathslover
    • 2 years ago
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    ok i got you now: actually i am present here from 3:00 PM to 9:00 PM (Indian Standard Time_ or there may be breaks but yes: There are gr8 experts present you don't need to care for your clarification of doubts. In case, if your doubt is not answered then you can post the link of your question in the chat. or tag some people having good smart score....

  11. mathslover
    • 2 years ago
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    lemme introduce you to some experts for your future help: experimentx mukushla Vaidehi09 amistre64 vishweshshrimali5 unklerhaukus and many more

  12. mathslover
    • 2 years ago
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    just put @ sign before there names and they will be looking on your question as soon as possible.

  13. mkumar441
    • 2 years ago
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    Another question ..Suppose A is an m by n matrix of rank r.Its reduced echelon form is R. Describe exactly reduced row echelon form of R transpose (not A transpose).

  14. mathslover
    • 2 years ago
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    Post that as a new question and tag me there.. I will help you there

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