Problem 4 Let A be an n x k matrix, for some positive integers n and k . Suppose we are given that rank(A) 0, with rank(A) + rank(A") + nullity(A) = and nullity(A) + nullity(A") + rank(A) = 7. Find the size of this matrix A , namely find n and k . Hint. Use some appropriate results for this, and be methodical in analyzing the situation.

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