8. We know that P₁ = P2 on B if P₁ = P₂ on C, provided that C generates B and is a 7-system. Show this last property cannot be omitted. For example, consider 2 = (a, b, c, d) with 1 P₁((a)) = P₁({d})= P2({b)) = P2({c)) = = and

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 1EQ: 1. Suppose that, in Example 2.27, 400 units of food A, 600 units of B, and 600 units of C are placed...
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8. We know that P₁ = P₂ on B if P₁ = P2 on C, provided that C generates B
and is a 7-system. Show this last property cannot be omitted. For example,
consider = (a, b, c, d) with
P₁({a})= P₁({d})= P2({b}) = P2({c});
16
and
P₁({b}) = P₁({c}) = P2({a}) = P2({d}) = 3·
C= [(a, b), (d, c), {a, c), (b, d)).
Set
Transcribed Image Text:8. We know that P₁ = P₂ on B if P₁ = P2 on C, provided that C generates B and is a 7-system. Show this last property cannot be omitted. For example, consider = (a, b, c, d) with P₁({a})= P₁({d})= P2({b}) = P2({c}); 16 and P₁({b}) = P₁({c}) = P2({a}) = P2({d}) = 3· C= [(a, b), (d, c), {a, c), (b, d)). Set
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