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Let f: R²R be defined by f((x, y)) = -8x - 7y. Is f a linear transformation? a. f((x1, y1) + (2, y2)) = = (Enter 2₁ as x1, etc.) f((x1, y₁)) + f((1T2, y2)) = -0+0 Does f((x1, y1)+(2, y2)) = f((x1, y₁)) + f((#2, y2)) for all (x1, y1), (2, y2) € R²? choose -0 -0(0) c(f((x, y))) = Does f(c(r, y)) = c(f((x, y))) for all c ER and all (x, y) = R²? choose b. f(c(x, y)) = c. Is f a linear transformation? choose

Let f: R²R be defined by f((x, y)) = -8x - 7y. Is f a linear transformation? a. f((x1, y1) + (2, y2)) = = (Enter 2₁ as x1, etc.) f((x1, y₁)) + f((1T2, y2)) = -0+0 Does f((x1, y1)+(2, y2)) = f((x1, y₁)) + f((#2, y2)) for all (x1, y1), (2, y2) € R²? choose -0 -0(0) c(f((x, y))) = Does f(c(r, y)) = c(f((x, y))) for all c ER and all (x, y) = R²? choose b. f(c(x, y)) = c. Is f a linear transformation? choose

Algebra and Trigonometry (6th Edition)
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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Let f: R²R be defined by f((x, y)) = -8x - 7y. Is f a linear transformation? a. f((x1, y1) + (2, y2)) = = (Enter 2₁ as x1, etc.) f((1, y₁)) + f((2, y2)) = 0+0 Does f((x, y) + (t2, y2)) = f((x1, y₁)) + f((t2, y2)) for all (x1, y1), (2, 2) E R²? choose -0 -0(0) Does f(c(r, y)) = c(f((x, y))) for all c ER and all (x, y) = R²? choose b. f(c(x, y)) = c(f((x, y))) = c. Is f a linear transformation? choose
Transcribed Image Text:Let f: R²R be defined by f((x, y)) = -8x - 7y. Is f a linear transformation? a. f((x1, y1) + (2, y2)) = = (Enter 2₁ as x1, etc.) f((1, y₁)) + f((2, y2)) = 0+0 Does f((x, y) + (t2, y2)) = f((x1, y₁)) + f((t2, y2)) for all (x1, y1), (2, 2) E R²? choose -0 -0(0) Does f(c(r, y)) = c(f((x, y))) for all c ER and all (x, y) = R²? choose b. f(c(x, y)) = c(f((x, y))) = c. Is f a linear transformation? choose
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