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Let V = sp({(1, 1, 1, 1)ª, (1, 1, 2, 4)¹, (0, –1, 6, 7)T}) ≤ R4. Find an orthonormal basis {u₁, U₂, U3} for V. Write the vector (3, 4, —2, −1)ª € V as a linear combination of u₁, U2, U3. Find the vector v € V closest to x = (4, 6, 1, 1)ª.

Let V = sp({(1, 1, 1, 1)ª, (1, 1, 2, 4)¹, (0, –1, 6, 7)T}) ≤ R4. Find an orthonormal basis {u₁, U₂, U3} for V. Write the vector (3, 4, —2, −1)ª € V as a linear combination of u₁, U2, U3. Find the vector v € V closest to x = (4, 6, 1, 1)ª.

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 71E
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4. Let V = sp({(1, 1, 1, 1)ª, (1, 1, 2, 4)¹, (0, −1, 6, 7)¹}) ≤ R¹. (a) Find an orthonormal basis {u₁, U2, u3} for V. (b) Write the vector (3,4, —2, −1)ª € V as a linear combination of u₁, U2, U3. (c) Find the vector v € V closest to x = = (4, 6, 1, 1)T.
Transcribed Image Text:4. Let V = sp({(1, 1, 1, 1)ª, (1, 1, 2, 4)¹, (0, −1, 6, 7)¹}) ≤ R¹. (a) Find an orthonormal basis {u₁, U2, u3} for V. (b) Write the vector (3,4, —2, −1)ª € V as a linear combination of u₁, U2, U3. (c) Find the vector v € V closest to x = = (4, 6, 1, 1)T.
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