Explain why the vectors u₁ = (2, 4,-4) U₂ = (-4,-8, 8) form a linearly dependent set of vectors in R³. (Solve this problem by inspection.) O The given vectors form a linearly dependent set since they are expressible as a linear combination of the standard basis vectors. O The given vectors form a linearly dependent set since U₁ + U₂ = U₂ + U₁. O The given vectors form a linearly dependent set since any two vectors in R³ form a linearly dependent set. O The given vectors form a linearly dependent set since u₁ + U₂ = (-2,-4, 4). O The given vectors form a linearly dependent set since u₂ = -2 u₁.

Explain why the vectors u₁ = (2, 4,-4) U₂ = (-4,-8, 8) form a linearly dependent set of vectors in R³. (Solve this problem by inspection.) O The given vectors form a linearly dependent set since they are expressible as a linear combination of the standard basis vectors. O The given vectors form a linearly dependent set since U₁ + U₂ = U₂ + U₁. O The given vectors form a linearly dependent set since any two vectors in R³ form a linearly dependent set. O The given vectors form a linearly dependent set since u₁ + U₂ = (-2,-4, 4). O The given vectors form a linearly dependent set since u₂ = -2 u₁.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.3: Spanning Sets And Linear Independence

Problem 35EQ

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