Orthogonal Complements: Prove the properties stated in Problems 1-2 using the following definition, illustrated by Fig. 3.5.4.
Question:
Let V be a subspace of Rn. A vector uÌ is orthogonal to subspace V provided that uÌ is orthogonal to every vector in V. The set of all vectors in Rn that are orthogonal to V is called the orthogonal complement of V, denoted
v´ = {uÌ ( Rn | uÌ ( vÌ = 0 for every vÌ ( V}.
Figure 3.5.4 An orthogonal complement uÌ
to a plane V
1. V´ is a subspace of Rn.
2. V © V´ = {0Ì
}
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Related Book For
Differential Equations and Linear Algebra
ISBN: 978-0131860612
2nd edition
Authors: Jerry Farlow, James E. Hall, Jean Marie McDill, Beverly H. West
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