Kunze Linear Algebra · Problem 3.1.1

Linear Transformations

Mathematics — Methods · linear-transformations-identification

Problem

Which of the following functions

T

from

R^2

into

R^2

are linear transformations? ((a))

T(x_1, x_2) = (1 + x_1, x_2)

; ((b))

T(x_1, x_2) = (x_2, x_1)

; ((c))

T(x_1, x_2) = (x_1^2, x_2)

; ((d))

T(x_1, x_2) = (\sin x_1, x_2)

; ((e))

T(x_1, x_2) = (x_1 - x_2, 0)