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

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#31

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
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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

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