1. Determine whether each of the following is a linear transformation.a. L: R3 → R2 defined by L(x,y,z) = (\x), y + z)b. L: M2x2 → P3 defined by L ( 2) = ax + (a + b)x? + (c + d)x+cC. L: R² → R³ defined by L(x,y) = (x + 1, 2y, x + y)

We have determine whether the following is a linear transformation

Answered: 1. Determine whether each of the…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Letf: R2 → R be defined by f((x, y)) = 7x + 7y + 1. Isf a linear transformation? a. f((x₁, y₁) + (x₂, y₂)) = b. f(c(x, y)) = f((x₁, y₁)) + f((x2, y₂)) = + Does f((x₁, y1) + (x₂, y₂)) = f((x₁, y₁)) + f((x2, y2)) for all (x₁, y₁), (x2, y2) ER2? choose . (Enter x₁ as x1, etc.) c(f((x, y))) = Does f(c(x, y)) = c(f((x, y))) for all c ER and all (x, y) = R²? choose c. Is f a linear transformation? choose Note: In order to get credit for this problem all answers must be correct. →
Let T: P → P, be the linear transformation satisfying T (x² + 8) = 3x² + 3x + 1, T (3x) = 12x, and T (2x – 7) = 8(x+ 9). Determine T (ax + bx + c), where a, b, and c are arbitrary real numbers.
I was given the wrong answer
8. Is there a linear transformation T: R³ → R² such that T(1, 0, 3) = (1, 1) and T(−2, 0, −6) = (2, 1) ? Explain.
5. A) Determine whether the given transformation is linear. STEP. T: R³ → R2x2 defined by (6) T = a1 2a2 + a1 a3 4a3a2
7. Let T : R² → R³ be a linear transformation with T(x1, x2) = (2x1 X2, -3x1 + - x2, 2x1 – 3x2). Can you find X (x1, x2) such that T(x1, x2) = (1,2, 3)?
2 Let T₁: P₂ → R² and T₂: R² → R2x2 be linear transformations defined as follows. Ti (az² + bx + c) = [a+b] ¹([2])-[ (T₂0 T₁) (2x² + 4x + 5) = 5х1 2x1 -9x2 -8x2 [ Ex: 42
Letf: R² → R be defined by f((x, y)) = -6x - 8y. Isf a linear transformation? a. f((x₁, y₁) + (x2, y₂)) = b. f(c(x, y)) = f((x₁, y₁)) + f((x₂, y₂)) = + Does f(x,y1) + (x₂, y2)) =f((x₁, y₁)) + f((x2, y2)) for all (x₁, y₁), (x₂, y2) E R²? choose (Enter x₁ as x1, etc.) c(f((x, y))) = Does f(c(x, y)) = c(f((x, y))) for all c ER and all (x, y) E R²? choose c. Isf a linear transformation? choose + + +
Let f: R R be defined by f((x, y)) = 7y - 3x - 3. Is f a linear transformation? a. f((x₁, y₁) + (x₂, y₂)) = etc.) f((x₁, y₁>) + f((x₂, y₂)) = + Does f((x1, y₁) + (x2, Y2 )) = f ((x₁, y₁ )) + f((x2, Y₂ )) for all (x₁, y₁), (x2, Y₂) E R ²? choose b. f (c(x, y)) = c(f((x, y))) = Does f(c(x, y)) = c(f ((x, y))) for all c ER and all (x, y) ER ²? choose c. Is f a linear transformation? choose . (Enter x₁ as x1, <
17. Let T R² R² be a linear transformation that maps [1] [3] 3 Tis linear to find the images under T of 3u, 2v, and 3u + 2v. u= into and maps v = into Use the fact that

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1. Determine whether each of the following is a linear transformation. a. L: R3 → R2 defined by L(x,y, z) = (Ix), y + z) b. L: M2x2 → P3 defined by L ( 2) = ax + (a + b)x? + (c + d)x +c C. L: R2 → R3 defined by L(x,y) = (x +1, 2y, x+ y)