Answered: Find an orthogonal basis for ℝ4 that…

Find an orthogonal basis for ℝ4 that contains the following vectors. [1 4 −1 0] and [1 0 1 3]. Hint set x3 = [0,0,1,0] and x4 = [0,0,0,1] and apply the Gramm-Schmidt Process.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.3: Orthonormal Bases:gram-schmidt Process

Problem 71E

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Question

Find an orthogonal basis for ℝ4 that contains the following vectors. [1 4 −1 0] and [1 0 1 3]. Hint set x3 = [0,0,1,0] and x4 = [0,0,0,1] and apply the Gramm-Schmidt Process.

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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