Let f : R? → R be defined by f((x, y)) = 5x + 7y. Is f a linear transformation?a. f({x1, Y1) + (x2, Y2)) =f(*1, Y1)) + f({x2; Y2)) =+Does f((*1, Y1) + (æ2, Y2)) = f((x1;Yı))+ f({x2; Y2)) for all (x1, Y1), (x2; Y2) e R?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?c. Is fa linear transformation?

Let † : R- → R be defined by f((x, Y)) = 5x + 7Y. Is ja linear transformation? (®1, Y1) + (x2, Y2)) %3D (®1, Y1)) + f(x2, Y2)) = + es f({¤1,Y1) + (x2, Y2)) = f((x1,Y1)) + f({x2, Y2)) for all (®1, Y1), (æ2, Y2) E R? c(x, y)) = f(x, y))) = mes f(c(x, y)) = c(f({x,y))) for all ce R and all (x, y) e R?

Let † : R- → R be defined by f((x, Y)) = 5x + 7Y. Is ja linear transformation? (®1, Y1) + (x2, Y2)) %3D (®1, Y1)) + f(x2, Y2)) = + es f({¤1,Y1) + (x2, Y2)) = f((x1,Y1)) + f({x2, Y2)) for all (®1, Y1), (æ2, Y2) E R? c(x, y)) = f(x, y))) = mes f(c(x, y)) = c(f({x,y))) for all ce R and all (x, y) e R?

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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