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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.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 70EQ
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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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