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.T(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)¹T

Given that .(a) We need to find an orthonormal basis of .(b) We need to write the vector as a…

Answered: Let V sp({(1, 1, 1, 1), (1, 1, 2, 4),…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Let {1, 2, 3, 4, 5, 6} be the standard basis in R6. Find the length of the vector = 3₁ - 22 - 2ě3 - 2ě4 – 2e5 - 3ē6. #
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Could you explain how to solve this linear algebra question?
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Let V sp({(1, 1, 1, 1), (1, 1, 2, 4), (0, -1, 6, 7)T}) CR¹. = ) Find an orthonormal basis {u₁, U2, U3} for V. U1, Write the vector (3, 4, -2, -1)¹ € V as a linear combination of ) Find the vector v € V closest to x = (4, 6, 1, 1)¹. U2, U3.