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Let X1 and X2 be two right inverses of a matrix A. a) Show that if...

Let X1 and X2 be two right inverses of a matrix A.

a) Show that if α + β = 1 then X = αX1 + βX2 is also a right inverse of A.

b) If we remove the condition that α + β = 1, could it be that sometimes X is a right inverse of A anyway? Either give an example to show that sometimes X can still be a right inverse even when α + β ≠1, or else prove that whenever α + β ≠ 1, X will never be a right inverse of A.

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