. Let L ⊂ R3 be the following subspace: L = {(x1, x2, x3) : x1 + x2 + 3x3 = 0}, and let ℓ be the linear functional given by ℓ(x1, x2, x3) = x1 − x2 + x3. Find the norm of the restriction of ℓ to L.

. Let L ⊂ R3 be the following subspace: L = {(x1, x2, x3) : x1 + x2 + 3x3 = 0}, and let ℓ be the linear functional given by ℓ(x1, x2, x3) = x1 − x2 + x3. Find the norm of the restriction of ℓ to L.

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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Question

. Let L ⊂ R3 be the following subspace:
L = {(x1, x2, x3) : x1 + x2 + 3x3 = 0},
and let ℓ be the linear functional given by
ℓ(x1, x2, x3) = x1 − x2 + x3.
Find the norm of the restriction of ℓ to L.

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