Kunze Linear Algebra · Problem 3.2.1

Linear Transformations

Mathematics — Methods · algebra-of-linear-operators

Problem

Let

T

and

U

be the linear operators on

R^2

defined by

T(x_1, x_2) = (x_2, x_1) \quad \text{and} \quad U(x_1, x_2) = (x_1, 0).

(a) How would you describe

T

and

U

geometrically? (b) Give rules like the ones defining

T

and

U

for each of the transformations

(U + T)

UT

TU

T^2

U^2