Determine whether the vectors v₁ =(4,-8, 12), and v₂ = (-5, 10, 15) are linearly independent; if linearly dependent, find a nontrivial linear combination of the form a₁v₁ + a₂v₂ that results in the zero vector. (Give a, and a₂ as real numbers. If the vectors are linearly independent, enter INDEPENDENT.) (a₁,₂)=

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question

lin comb

Determine whether the vectors V₁ = (4, -8, 12), and v₂ = (-5, 10, −15) are linearly independent; if linearly dependent, find a nontrivial linear combination of the form a₁v₁ + a₂v₂ that
results in the zero vector. (Give a, and a2 as real numbers. If the vectors are linearly independent, enter INDEPENDENT.)
(a₁,₂)= (
Transcribed Image Text:Determine whether the vectors V₁ = (4, -8, 12), and v₂ = (-5, 10, −15) are linearly independent; if linearly dependent, find a nontrivial linear combination of the form a₁v₁ + a₂v₂ that results in the zero vector. (Give a, and a2 as real numbers. If the vectors are linearly independent, enter INDEPENDENT.) (a₁,₂)= (
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
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,