Consider the following vector subspace of R 3 : a).Find a base for W. b).Is the base you found for W in the previous item orthogonal? c).Find the orthogonal complement of W. d).Find an orthonormal basis for the orthogonal complement of W.

Consider the following vector subspace of R 3 : a).Find a base for W. b).Is the base you found for W in the previous item orthogonal? c).Find the orthogonal complement of W. d).Find an orthonormal basis for the orthogonal complement of W.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.1: Rectangular Coordinate Systems

Problem 35E

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Question

Consider the following vector subspace of R³ :
a).Find a base for W.
b).Is the base you found for W in the previous item orthogonal?
c).Find the orthogonal complement of W.
d).Find an orthonormal basis for the orthogonal complement of W.

W = Span{(1, 1,0), (0, 1, 1), (1,0, – 1), (1, –1, –2)}
%3D

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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