2. Let V = R" and let {e1,...,en} be the standard basis for V. a) Give an example of a subspace of V that has dimension m for each 1 < m < n. b) Let U = Span(v1, V2, - .. , Un) where vi = e1 and Vi = e1 + e; for 2

2. Let V = R" and let {e1,...,en} be the standard basis for V. a) Give an example of a subspace of V that has dimension m for each 1 < m < n. b) Let U = Span(v1, V2, - .. , Un) where vi = e1 and Vi = e1 + e; for 2

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 V = R^n and let {e1, . . . , en} be the standard basis for V.
a) Give an example of a subspace of V that has dimension m for each 1 <= m <= n.
b) Let U = Span(v1, v2, . . . , vn) where v1 = e1 and
vi = e1 + ei for 2 <= i <= n.
What is the dimension of U?

2. Let V = R" and let {e1,..., en} be the standard basis for V.
a) Give an example of a subspace of V that has dimension m for each 1 <m < n.
b) Let U = Span(v1, v2,..., Un) where vi = e1 and
Vị = €1 + e; for 2 <i< n.
What is the dimension of U?

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