Texts:
1. Show that the transformation T: R^2 → R^2 defined by T(x1, x2) = (4x1 - 2x2, 3|x2|) is not linear.
2. Find an example of two functions f: R^m → R^n and g: R^n → R^p such that neither f nor g is a linear transformation, but g ◦ f is a linear transformation. Carefully justify your answer.
3. The following statement is false: If S: R^n → R^m is a linear transformation, then range(S) = R^m. Prove this statement is false by constructing a counterexample and justify your answer.