Question: Let A be a 2 2 matrix, and let LA be the linear operator defined by LA(x) = Ax Show that (a) LA maps

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

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