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Math Help - linear algebra proofs

  1. #1
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    [PROVED] linear algebra proofs

    I want to show that rank(A+B) \leq rank(A)+rank(B) where A,B \in M_{m,n}(R).

    It is obvious that rank(A), rank(B), rank(A+B) are \leq m. So, rank(A)+rank(B) \leq 2m, rank(A+B) \leq m. Can I conclude now that rank(A+B) \leq rank(A)+rank(B)? I think there should be somemore steps to continue this proof.


    Next questions, I need some hints.
    Let u_{1},...,u_{k},v_{1},...v_{n} \in R^{n}. If each vector u_{i} is a linear combination of vectors of v_{1},...,v_{n}. Show that the maximum number of linearly independent vectors in \{u_{1},...,u_{k}\} cannot exceed the maximum number of linearly independent vectors in \{v_{1},...,v_{n}\}
    Last edited by deniselim17; April 2nd 2010 at 09:26 PM.
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  2. #2
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    Exclamation

    it's urgent. Can anyone help???
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  3. #3
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    I proved both of them.
    Thank you anyway.
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