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You'll need to complete a few actions and gain 15 reputation points before being able to upvote Show that im(a⊤) = ker(a)⊥ im (a ⊤) = ker (a) ⊥. Upvoting indicates when questions and answers are useful

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Suppose some matrices a ∈rn×n a ∈ r n × n with rank(a) = r r a n k (a) = r and b ∈rn×(n−r) b ∈ r n × (n − r) satisfies ker(a) = im(b) k e r (a) = i m (b)

In this situation, i thought.