Explain why the vectors U₁=(3, 8, -8) U₂ = (-12, -32, 32) form a linearly dependent set of vectors in R³. (Solve this problem by inspection.) The given vectors form a linearly dependent set since u₂ = -4 ₁. 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 = (-9, -24, 24). 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 = U₂+U₁.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
Explain why the vectors
U₁ = (3, 8, -8)
U₂ = (-12, -32, 32)
form a linearly dependent set of vectors in R³. (Solve this problem by inspection.)
The given vectors form a linearly dependent set since u₂ = -4 u₁.
The given vectors form a linearly dependent set since they are expressible as a linear combination of the standard basis
vectors.
The given vectors form a linearly dependent set since U₁+U₂ = (-9, -24, 24).
The given vectors form a linearly dependent set since any two vectors in R³ form a linearly dependent set.
The given vectors form a linearly dependent set since ₁ + U2 = U2+ U1.
Transcribed Image Text:Explain why the vectors U₁ = (3, 8, -8) U₂ = (-12, -32, 32) form a linearly dependent set of vectors in R³. (Solve this problem by inspection.) The given vectors form a linearly dependent set since u₂ = -4 u₁. The given vectors form a linearly dependent set since they are expressible as a linear combination of the standard basis vectors. The given vectors form a linearly dependent set since U₁+U₂ = (-9, -24, 24). The given vectors form a linearly dependent set since any two vectors in R³ form a linearly dependent set. The given vectors form a linearly dependent set since ₁ + U2 = U2+ U1.
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Similar questions
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,