(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

given two matrices A, B of 5x5 order:

[itex]\rho(A)<\rho(B)[/itex]

the nullspace for A is [itex]Sp{(0, 3, -1, 2, 1),(4, -2, 1, 4, 0)}[/itex]

prove that

[itex]AB\neq 0[/itex]

2. Relevant equations

[itex]\rho(A)=n- \rho(P_a)[/itex]

3. The attempt at a solution

so I now that the nullity is 2 and so [itex]\rho(A)=3[/itex]

and because of that [itex]4\leq \rho(B)\leq 5[/itex]

but I don't know how to prove that [itex]AB\neq 0[/itex]

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# Linear Algebra - Ranks and dimension

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