Question: Let A be an m n matrix. Suppose that C = (A B ) is an m (n + k) matrix whose first

Let A be an m × n matrix. Suppose that C = (A B ) is an m × (n + k) matrix whose first n columns are the same as A. Prove that mgC ⊇ mg A. Thus, appending more columns cannot decrease the size of a matrix's range. Give an example where mgC ≠ rng A.

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