Principles of Quantum Mechanics · Problem 1.1.2

Mathematical Introduction — R. Shankar

Physics — Quantum Mechanics · linear-vector-spaces

Problem

Consider the set of all entities of the form

(a, b, c)

where the entries are real numbers. Addition and scalar multiplication are defined as follows:

(a, b, c) + (d, e, f) = (a+d, b+e, c+f)

a(a, b, c) = (aa, ab, ac).

Write down the null vector and inverse of

(a, b, c)

. Show that vectors of the form

(a, b, 1)

do not form a vector space.