Let L: R? → R² be defined by L(2) – 1 () - (**) T1 + x2 = L = We want to show that L is a linear transformation by showing that L(ax + by) = aL(æ)+ bL(y) for all scalars a, b. We'll first compute the left side of this equation in two steps (remembering to use WebWork's angular bracket notation (e.g., (x1, x2)) for vectors. Enter subscripted variables a1 as rl.): aæ + by = a (r1, x2) + b (y1, y2) Now take L of the preceding vector to get: L(aæ + by) OK, now let's compute the right side of the equation. First, aL(æ): and bL(y) So aL(æ) + bL(y) If your answers are correct, the two sides should be equal.

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