An m ×n matrix A is said to have a right inverse if there exists an n ×m matrix C such that AC = Im. A is said to have a left inverse if there exists an n × m matrix D such that DA = In.
(a) Show that if A has a right inverse, then the column vectors of A span Rm.
(b) Is it possible for an m×n matrix to have a right inverse if n < m? n ≥ m? Explain.
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