Problem

Let A be a 2 × 2 matrix, and let LA be the linear operator defined by L A (...

Let A be a 2 × 2 matrix, and let LA 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 LA maps R2 onto R2.

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Solutions For Problems in Chapter 4.1