Riley hobson bence · Problem 1.32

Preliminary algebra

Mathematics — Methods · necessary-sufficient-conditions-linear-equations

Problem

Given that at least one of

a

and

b

, and at least one of

c

and

d

, are non-zero, show that

ad = bc

is both a necessary and sufficient condition for the equations

ax + by = 0,

cx + dy = 0,

to have a solution in which at least one of

x

and

y

is non-zero.