Answered: Let T : R^3 --> R^3 be a linear…

Let T : R^3 --> R^3 be a linear transformation that reflects each vector x = (x1,x2 ,x3) through the plane x3 = 0 onto T(x) = (x1,x2,-x3). Show that T is a linear transformation.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.3: Matrices For Linear Transformations

Problem 52E: Let T be a linear transformation T such that T(v)=kv for v in Rn. Find the standard matrix for T.

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Let T : R^3 --> R^3 be a linear transformation that reflects each vector x = (x1,x2 ,x3) through the plane x3 = 0 onto T(x) = (x1,x2,-x3). Show that T is a linear transformation.

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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