Let f : R? → R be defined by f((x,y)) = 8y – 2x. Is f a linear transformation?a. f(x1, Yı) + (*2, Y2)). (Enter x1 as x1, etc.)f(r1, Y1)) + f((x2, Y2) ) =+Does f((x1, Y1) + (x2; Y2)) = f((¤1, Y1)) + f((x2, Y2)) for all (21, Y1), (x2, Y2) E R?? chooseb. 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? choosec. Is f a linear transformation? choose

The objective of the question is examine the linear transformation.

Let f : R? → R be defined by f((x,y)) = 8y – 2x. Is f a linear transformation? a. f({®1, Y1) + (x2, Y2)) = (Enter x1 as x1, etc.) f((1, Y1}) + f((w2, Y2)) = + Does f(*1, Y1) + (#2, Y2)) = f((x1, Y1)) + f((x2, Y2)) for all (x1, Y1), (x2, Y2) E R?? choose b. f(c(x, y)) c(f({r, y))) = Does f(c(x, y)) = c(f({x,y))) for all c € R and all (x, y) E R? choose c. Is fa linear transformation? choose

Let f : R? → R be defined by f((x,y)) = 8y – 2x. Is f a linear transformation? a. f({®1, Y1) + (x2, Y2)) = (Enter x1 as x1, etc.) f((1, Y1}) + f((w2, Y2)) = + Does f(*1, Y1) + (#2, Y2)) = f((x1, Y1)) + f((x2, Y2)) for all (x1, Y1), (x2, Y2) E R?? choose b. f(c(x, y)) c(f({r, y))) = Does f(c(x, y)) = c(f({x,y))) for all c € R and all (x, y) E R? choose c. Is fa linear transformation? choose

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.4: Linear Transformations

Problem 12EQ

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