Prove that the vectors (?\index{1},?\index{2}), (?\index{1},?\index{2})∈R×R are linearly dependent iff ?\index{1}?\index{2}-?\index{2}?\index{1}=0. Prove that the vectors (a₁, a2), (B₁, B₂) € R× Rarelinearly dependent iff a₁ß2-a2ß₁ = 0.

The given vectors are and We have to show that the given vector is linearly dependent if

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Prove that the vectors (a1, a2), (B₁, B₂) = R× Rare linearly dependent iff α₁ß2 - α2ß₁ = 0.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.CR: Review Exercises

Problem 78CR: Let v1, v2, and v3 be three linearly independent vectors in a vector space V. Is the set...

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Question

Prove that the vectors (?\index{1},?\index{2}), (?\index{1},?\index{2})∈R×R are
linearly dependent iff ?\index{1}?\index{2}-?\index{2}?\index{1}=0.

Prove that the vectors (a₁, a2), (B₁, B₂) € R× Rare
linearly dependent iff a₁ß2-a2ß₁ = 0.

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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