Let f : R → R° be defined by f(x) = (-2x, 7x, 7x). Is ƒ a linear transformation? a f(r + y) f(r)+ f(y) Does f(r + y) = f(r)+ f(y) for all T, Y E R? choose b. f(cz) = c(f(z)) = Does f(cz) = c(f(x)) for all c, x E R? choose c. Is fa linear transformation? choose

Let f : R → R° be defined by f(x) = (-2x, 7x, 7x). Is ƒ a linear transformation? a f(r + y) f(r)+ f(y) Does f(r + y) = f(r)+ f(y) for all T, Y E R? choose b. f(cz) = c(f(z)) = Does f(cz) = c(f(x)) for all c, x 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

Section6.5: The Kernel And Range Of A Linear Transformation

Problem 4EQ

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Question

Filling in the blanks for part a, b and c

For part a and b, where it says "choose" the options are
1) yes they are equal
2) no they are not equal

For part c, where it says "choose" the options are
1) f is a linear transformation
2) f is not a linear transformation

Let f : R → R° be defined by f(x) = (-2x, 7x, 7x). Is fa linear transformation?
a. f(x + y) =
f(x) + f(y) =
+
Does f(r + y) = f(x)+ f(y) for all x, y E R? choose
b. f(cx) =
c(f(x)) =
Does f(cx) = c(f(x)) for all c, r e R? choose
c. Is fa linear transformation? choose

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