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Question: please follow the comment and explain it step by step...

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Please follow the comment and explain it step by step

Let A be a 2 × 2 matrix, and let LA be the linear
operator defined by
L(x) = Ax
Show that
(a) L maps R2 onto the column space of A.
(b) if A is nonsingular, then LA maps R2 onto R2

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