7 Consider the system Ax g and any c inverse A c of the m x n matrix A Let h 1 , h 2 , , h r be any set of vectors from E n , and let c 1 , c 2 , , c r be any set of scalars Show that if the system is consistent the vector y is a solution to the system where y A c g i 1 r c i (I A c A)h i ...

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7. Consider the system Ax = g and any c-inverse A c of the m x n

Question:

7. Consider the system Ax = g and any c-inverse A^c of the m x n matrix A. Let h₁, h₂,..., h_r be any set of vectors from E_n, and let c₁, c₂,..., c_r be any set of scalars. Show that if the system is consistent the vector y is a solution to the system where y = A^cg + ∑_i=1^rc_i(I - A^cA)h_i.