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Let f : R? → R be defined by f((x, y)) = 9x – 7y. Is f a linear transformation? a. f((r1, Y1) + (x2, Y2)) =| - (Enter æ1 as x1, etc.) f((x1, Y4)) + f({x2; 42)) = + Does f((x1, y1) + (æ2, Y2)) = f(x1, y1)) + f((x2; Y2)) for all (x1, Y1), (x2; Y2) E R? choose choose b. f(c(x, y)) = Yes, they are equal No, they are not equal c(f((x, y))) Does f(c{x, y)) = c(f((x, y))) for all c e R and all (x, y) e R²? choose c. Is f a linear transformation? choose

Let f : R? → R be defined by f((x, y)) = 9x – 7y. Is f a linear transformation? a. f((r1, Y1) + (x2, Y2)) =| - (Enter æ1 as x1, etc.) f((x1, Y4)) + f({x2; 42)) = + Does f((x1, y1) + (æ2, Y2)) = f(x1, y1)) + f((x2; Y2)) for all (x1, Y1), (x2; Y2) E R? choose choose b. f(c(x, y)) = Yes, they are equal No, they are not equal c(f((x, y))) Does f(c{x, y)) = c(f((x, y))) for all c e R and all (x, y) e R²? choose c. Is f a linear transformation? choose

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.5: The Kernel And Range Of A Linear Transformation
Problem 4EQ
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The option for a is the same as for b

Let f : R? → R be defined by f((x, y)) = 9x – 7y. Is f a linear transformation? a. f({x1,Y1) + (x2, Y2)) (Enter x1 as x1, etc.) f((x1, 41)) + f({x2; Y2)) : Does f((x1,Y1) + (x2, Y2)) = f({x1; Y1)) + f(x2, Y2)) for all (x1, Y1), (x2, Y2) E R?? choose b. f(c{x, y)) c(f((x, y))) Does f(c(x, y)) = c(f({x, y))) for all c e R and all (x, y) e R²? choose c. Is f a linear transformation? choose choose f is a linear transformation f is not a linear transformation
Transcribed Image Text:Let f : R? → R be defined by f((x, y)) = 9x – 7y. Is f a linear transformation? a. f({x1,Y1) + (x2, Y2)) (Enter x1 as x1, etc.) f((x1, 41)) + f({x2; Y2)) : Does f((x1,Y1) + (x2, Y2)) = f({x1; Y1)) + f(x2, Y2)) for all (x1, Y1), (x2, Y2) E R?? choose b. f(c{x, y)) c(f((x, y))) Does f(c(x, y)) = c(f({x, y))) for all c e R and all (x, y) e R²? choose c. Is f a linear transformation? choose choose f is a linear transformation f is not a linear transformation
Let f : R? → R be defined by f((x, y)) = 9x – 7y. Is f a linear transformation? a. f((x1,Y1) + (x2, Y2)) (Enter x1 as x1, 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?? choose choose Yes, they are equal No, they are not equal b. f(c(x, y)) c(f({x, y))) Does f(c{x, y)) = c(f((x, y))) for all c e R and all (x, y) e R? choose c. Is f a linear transformation? choose
Transcribed Image Text:Let f : R? → R be defined by f((x, y)) = 9x – 7y. Is f a linear transformation? a. f((x1,Y1) + (x2, Y2)) (Enter x1 as x1, 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?? choose choose Yes, they are equal No, they are not equal b. f(c(x, y)) c(f({x, y))) Does f(c{x, y)) = c(f((x, y))) for all c e R and all (x, y) e R? choose c. Is f a linear transformation? choose
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