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Let A ∈ Rmxn, and B ∈ Rrxm. Show that BR(A) = R(BA), where BR(A) :=...

Let A ∈ Rmxn, and B ∈ Rrxm. Show that BR(A) = R(BA), where BR(A) := {Bz | z ∈ R(A)},

and use this result to show that BR(A) is a subspace of Rr.

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