(i) Prove that(1, 2, 1) , (2, 1, 5) , (1, –4,7)is linear dependent subset of R³.(ii) Determine whether the vector (1,6, 2) is a linear combination of the vectors (1,2, –1), (3, 1, 1),and (-4,0, 6). (Include all the steps in your reasoning.).

A set is linearly dependent if and only if one vector is linear combination of other vectors.

Answered: { (1, 2, 1), (2, 1, 5) , (1, –4, 7) }…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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{ (1, 2, 1), (2, 1, 5) , (1, –4, 7) } (i) Prove that is linear dependent subset of R³. (ii) Determine whether the vector (1,6, 2) is a linear combination of the vectors (1, 2, –1), (3, 1, 1), and (-4,0, 6). (Include all the steps in your reasoning.).