MathDB

IMC 1998 Problem 7

Source: IMC 1998 Day 2 Problem 1

October 28, 2020

linear algebra

Problem Statement

V

is a real vector space and

f, f_{i}: V \rightarrow \mathbb{R}

are linear for

i = 1, 2, ... , k.

Also

f

is zero at all points for which all of

f_{i }

are zero. Show that

f

is a linear combination of the

f_{i}

.

Back to Problems View on AoPS