Consider the three sets: {D} (a) For each set above, determine if it is an orthogonal set and if it is a basis for R. (b) A normal basis consists of vectors length one and an orthonormal basis consists of vectors that are orthogonal to one another and length one. Convert an orthogonal basis from above into an orthonormal basis {ủ1, ū2, ūz} (without changing the direction of the vectors).

Consider the three sets: {D} (a) For each set above, determine if it is an orthogonal set and if it is a basis for R. (b) A normal basis consists of vectors length one and an orthonormal basis consists of vectors that are orthogonal to one another and length one. Convert an orthogonal basis from above into an orthonormal basis {ủ1, ū2, ūz} (without changing the direction of the vectors).

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 17E: Complete Example 2 by verifying that {1,x,x2,x3} is an orthonormal basis for P3 with the inner...

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