Let A be a 2 2 matrix, and let L A be the linear operator defined by L A(x) = Ax Show

Chapter 4, Problem 24

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

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