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Show that the dot product distributes over vector addition. Statement: Let ū, i, w be vectors in R". Then: Proof: Let i = < %3D Then: 3+ w = < > so, i o (i + w) = u,(v, + w,) + The distributive property for real numbers says that: %3D Therefore: u, (v1 + w1) = u1v1 + II

Show that the dot product distributes over vector addition. Statement: Let ū, i, w be vectors in R". Then: Proof: Let i = < %3D Then: 3+ w = < > so, i o (i + w) = u,(v, + w,) + The distributive property for real numbers says that: %3D Therefore: u, (v1 + w1) = u1v1 + II

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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Please help me with this proof. Thank you!

and uz(v2 + w2) = un(Vn + Wn) =. which equals (u,v, + .…+ unVn) + = ū •- +
Transcribed Image Text:and uz(v2 + w2) = un(Vn + Wn) =. which equals (u,v, + .…+ unVn) + = ū •- +
Show that the dot product distributes over vector addition. Statement: Let ū, i, w be vectors in R". Then: Proof: Let Then: 3 + w = < > so, i o (i + w) = u,(v, + w,) + The distributive property for real numbers says that: Therefore: u, (v, + w;) = u1V1 + II 13
Transcribed Image Text:Show that the dot product distributes over vector addition. Statement: Let ū, i, w be vectors in R". Then: Proof: Let Then: 3 + w = < > so, i o (i + w) = u,(v, + w,) + The distributive property for real numbers says that: Therefore: u, (v, + w;) = u1V1 + II 13
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