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Let {u₁, U2, u2} be an orthonormal basis for an inner product space V. Suppose v = au₁ + bu₂ + cuz is so that ||v||= √80, (v, u₂) = -8, and (v, u3) 4. Find the possible values for a, b, and c. a= b= C=

Let {u₁, U2, u2} be an orthonormal basis for an inner product space V. Suppose v = au₁ + bu₂ + cuz is so that ||v||= √80, (v, u₂) = -8, and (v, u3) 4. Find the possible values for a, b, and c. a= b= C=

Elementary Linear Algebra (MindTap Course List)
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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Let {u₁, 12, u2} be an orthonormal basis for an inner product space V. Suppose v = au₁ + bu₂ + cuz is so that ||v||= √80, (v, u₂) = -8, and (v, u3) = -4. Find the possible values for a, b, and c. a= b= .c
Transcribed Image Text:Let {u₁, 12, u2} be an orthonormal basis for an inner product space V. Suppose v = au₁ + bu₂ + cuz is so that ||v||= √80, (v, u₂) = -8, and (v, u3) = -4. Find the possible values for a, b, and c. a= b= .c
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