Let W = {(x − y − z, y − z, x + y − z) | x, y, z ∈ R} ⊂ R3 be a vector subspace. Do the following (justify your answers). (a) Determine a generating set for W; (b) Using the previous item, extract a basis for the vector space W.

Let W = {(x − y − z, y − z, x + y − z) | x, y, z ∈ R} ⊂ R3 be a vector subspace. Do the following (justify your answers). (a) Determine a generating set for W; (b) Using the previous item, extract a basis for the vector space W.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.CR: Review Exercises

Problem 73CR

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Question

Let W = {(x − y − z, y − z, x + y − z) | x, y, z ∈ R} ⊂ R³ be a vector subspace. Do the following (justify your answers).

(a) Determine a generating set for W;

(b) Using the previous item, extract a basis for the vector space W.

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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