Question: Let L:Rn --> Rm be a linear transformation. Prove that there exists matrix A (element of Rmxn) such that L(X) = A*x for all x(element

Let L:Rn --> Rm be a linear transformation. Prove that there exists matrix A (element of Rmxn) such that

L(X) = A*x for all x(element of Rn),

nullspace(A) = ker(L) ,

and

collspace(A) = image(L).

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