Let be the set of continuous real functions on with

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Linear algebra and vector spaces · Linear algebra and vector spaces

Mathematical Methods for Physics, Ch Vector spaces, bases, linear maps and dual vectors

Problem

Let SS be the set of continuous real functions ff on [0,L][0,L] with f(0)=T0f(0) = T_0, a fixed nonzero constant, together with the usual addition of functions and multiplication by a real scalar. ((a)) Take any two members f1,f2∈Sf_1,f_2\in S, evaluate (f1+f2)(0)(f_1+f_2)(0), and decide whether f1+f2f_1+f_2 belongs to SS. ((b)) Evaluate (cf1)(0)(cf_1)(0) for a real scalar c≠1c\ne1 and decide whether cf1cf_1 belongs to SS. ((c)) Name the requirement or rule (or rules) that fail, and state the one change to the value fixed at x=0x=0 that would make SS a vector space.

Browse the problem library