Use row coefficients=[13, -1] and primal vector=[2, 15] in one fixed coordinate basis. Coordinates are exact rationals, written as integers or [numerator, denominator] pairs with nonzero denominator. Give (coefficients, vector, value, boundary).
G001 — Use row coefficients=[13, -1] and primal vector=[2, 15] in one fixed coordinate basis. Coordinates are exact rationals, written as integers or [numerator, denominator] pairs with nonzero denominator. Give (coefficients, vector, value, boundary).
Definition and scope
Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.
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fixed original covector ROW=[13, -1];coordinate dimension=2
After
define phi(x)=sum_j row[j]*x[j] for EVERY real coordinate vector x;finite distributivity gives phi(alpha*u+beta*v)=alpha*phi(u)+beta*phi(v)
Conditions: none
Finite distributivity for a fixed row holds for arbitrary real u,v,alpha,beta and gives the universal linearity certificate.The subsequent substitution checks this instance,not linearity of an unspecified function from one passing test.The row represents a real-valued function,not the primal vector itself.
The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.
This question review and source binding
Review date: 2026-10-26
Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.