Help 3. In R³, consider V₁ = (1, 0, −1), V₂ = (1,0, 2), V3 = (0,1,1), V₁ = (1, −1, 1).(a) Show that any vector (x, y, z) = R³ can be expressed as a linear combi-nation of the vectors U₁, V2, V3.(b) Find another triplet of the vectors such that the same is no longer achiev-able.

Answered: Image /qna-images/answer/9777c4dd-3521-4a9d-9797-bcfab55fd1f3.jpg

3. In R³, consider v₁ = (1,0, -1), V₂ = (1, 0,2), V3 = (0, 1, 1), №₁ = (1, −1, 1). (a) Show that any vector (x, y, z) = R³ can be expressed as a linear combi- nation of the vectors V₁, V2, V3. (b) Find another triplet of the vectors such that the same is no longer achiev- able

3. In R³, consider v₁ = (1,0, -1), V₂ = (1, 0,2), V3 = (0, 1, 1), №₁ = (1, −1, 1). (a) Show that any vector (x, y, z) = R³ can be expressed as a linear combi- nation of the vectors V₁, V2, V3. (b) Find another triplet of the vectors such that the same is no longer achiev- able

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.1: Length And Dot Product In R^n

Problem 17E: Consider the vector v=(1,3,0,4). Find u such that a u has the same direction as v and one-half of...

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Question

Help

3. In R³, consider V₁ = (1, 0, −1), V₂ = (1,0, 2), V3 = (0,1,1), V₁ = (1, −1, 1).
(a) Show that any vector (x, y, z) = R³ can be expressed as a linear combi-
nation of the vectors U₁, V2, V3.
(b) Find another triplet of the vectors such that the same is no longer achiev-
able.

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