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53. Consider a subspace V of R". We define the orthogo- nal complement V- of V as the set of those vectors w in R" that are perpendicular to all vectors in V; that is, w .i = 0, for all i in V. Show that V- is a subspace of R". 54. Consider the line L spanned by 2 in R. Find a basis 3 of L-. See Exercise 53.

53. Consider a subspace V of R". We define the orthogo- nal complement V- of V as the set of those vectors w in R" that are perpendicular to all vectors in V; that is, w .i = 0, for all i in V. Show that V- is a subspace of R". 54. Consider the line L spanned by 2 in R. Find a basis 3 of L-. See Exercise 53.

Advanced Engineering Mathematics
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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a e f 53. Consider a subspace V of R". We define the orthogo- nal complement V- of V as the set of those vectors w in R’ that are perpendicular to all vectors in V; that is, w.ū = 0, for all i in V. Show that V- is a subspace of R". 54. Consider the line L spanned by 2 in R´. Find a basis 3 of L-. See Exercise 53.
Transcribed Image Text:a e f 53. Consider a subspace V of R". We define the orthogo- nal complement V- of V as the set of those vectors w in R’ that are perpendicular to all vectors in V; that is, w.ū = 0, for all i in V. Show that V- is a subspace of R". 54. Consider the line L spanned by 2 in R´. Find a basis 3 of L-. See Exercise 53.
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