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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.

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.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.CR: Review Exercises
Problem 21CR: Let T be a linear transformation from R2 into R2 such that T(4,2)=(2,2) and T(3,3)=(3,3). Find...
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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.
Transcribed Image Text: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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