Linear Algebra Done Right · Problem 1C.4

Finite-Dimensional Vector Spaces — Sheldon Axler

Mathematics — Linear Algebra · subspaces

Problem

Suppose

b \in \mathbf{R}

. Show that the set of continuous real-valued functions

f

on the interval

[0, 1]

such that

\int_0^1 f = b

is a subspace of

\mathbf{R}^{[0,1]}

if and only if

b = 0