Define the relation Ron R X Ras (V(x, y), (u, v) =RxR (x, y) R (u, v) iff y - x = v - u. 1. Show that R is an equivalence relation on R × R. 2. Determine [(1, 1)]. COMPLETE SOLUTIONS TYPEWRITTEN OR WRITE LEGIBLY UNCLEAR SOLUTIONS WILL GET A LOW RATING

Elementary Linear Algebra (MindTap Course List)
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ISBN:9781305658004
Author:Ron Larson
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Chapter5: Inner Product Spaces
Section5.CM: Cumulative Review
Problem 4CM: Use a software program or a graphing utility to write v as a linear combination of u1, u2, u3, u4,...
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Define the relation R on RX Ras
(V(x, y), (u, v) ≤ R ×R (x, y) R (u, v) iff y - x = v — u.
1. Show that is an equivalence relation on RX R.
2. Determine [(1,1)]R.
COMPLETE SOLUTIONS
TYPEWRITTEN OR WRITE LEGIBLY
UNCLEAR SOLUTIONS WILL GET A LOW RATING
Transcribed Image Text:Define the relation R on RX Ras (V(x, y), (u, v) ≤ R ×R (x, y) R (u, v) iff y - x = v — u. 1. Show that is an equivalence relation on RX R. 2. Determine [(1,1)]R. COMPLETE SOLUTIONS TYPEWRITTEN OR WRITE LEGIBLY UNCLEAR SOLUTIONS WILL GET A LOW RATING
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