Let W be the subspace of R4 orthogonal to u1=(2, 1, -2, 2) and u2=(0, 2, -2, 1), that is, W=S⊥, where S={u1=( 2, 1, -2, 2), u2=(0, 2, -2,1)}. Find (a) a basis and the dimension) of the subspace W. (b): an orthogonal basis of the subspace W.

Let W be the subspace of R4 orthogonal to u1=(2, 1, -2, 2) and u2=(0, 2, -2, 1), that is, W=S⊥, where S={u1=( 2, 1, -2, 2), u2=(0, 2, -2,1)}. Find (a) a basis and the dimension) of the subspace W. (b): an orthogonal basis of the subspace W.

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 W be the subspace of R4 orthogonal to u1=(2, 1, -2, 2) and u2=(0, 2, -2, 1), that is, W=S^⊥,
where S={u1=( 2, 1, -2, 2), u2=(0, 2, -2,1)}. Find
(a) a basis and the dimension) of the subspace W.
(b): an orthogonal basis of the subspace W.

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