Hey Guys, Another matrice question(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

Prove: Rk(A+B)[tex]\leq[/tex] Rk(A) +Rk(B)

3. The attempt at a solution

Rk(A+B) = Dim[R(A) + R(B)]

Where R(A) is the row space of A

we know that Dim[R(A)+R(B)] = Dim[R(A)] + Dim[R(B)] - Dim[R(A)[tex]\cap[/tex]R(B)]

Which means that Dim[R(A)+R(B)] [tex]\leq[/tex] Dim[R(A)] + Dim[R(B)] iff Rk(A+B)[tex]\leq[/tex] Rk(A) +Rk(B)

I heard a rumor that this can also be done with linear transformations, can anyone elighten me on that path?

Is this correct?

Thanks

Tal

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Matrix rank question

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