31. An m x n matrix A is said to have a right inverse if there exists annxm matrix C such that AC Im The matrix A is said to have a left inverse if there exists an n x m matrix D such that DA = Iq....

#31

Extracted text: 31. An m x n matrix A is said to have a right inverse if there exists annxm matrix C such that AC Im The matrix A is said to have a left inverse if there exists an n x m matrix D such that DA = Iq. (a) Show that if A has a right inverse, then the column vectors of A span R" (b) Is it possible for an mx n matrix to have a right inverse if n m? n 2 m? Explain