(a) determine whether the set of vectors in Rn is orthogonal, (b) if the set is orthogonal, then determine whether it is also orthonormal,(c) determine whether the set is a basis for Rn.{(2, −4), (2, 1)}

(a) determine whether the set of vectors in Rn is orthogonal, (b) if the set is orthogonal, then determine whether it is also orthonormal,(c) determine whether the set is a basis for Rn.{(2, −4), (2, 1)}

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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Question

(a) determine whether the set of vectors in Rⁿ is orthogonal,
(b) if the set is orthogonal, then determine whether it is also orthonormal,
(c) determine whether the set is a basis for Rⁿ.

{(2, −4), (2, 1)}

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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