This example considers the special case where there are exactly two vector and from some real or complex vector space. The vectors and are linearly dependent if and only if at least one of the following is true: is a scalar multiple of (explicitly, this means that there exists a scalar such that ) or is a scalar multiple of (explicitly, this means that there exists a scalar such that ). If then by setting we have (this equality holds no matter what the value of is), which shows that (1) is true in this particular case. Similarly, if then (2) is true because If (for instance, if they are both equal to the zero vector ) then both (1) and (2) are true (by using for both).
This example considers the special case where there are exactly two vector and from some real or complex vector space. The vectors and are linearly dependent if and only if at least one of the following is true: is a scalar multiple of (explicitly, th!is means that there exists a scalar such that ) or is a scalar! multiple of (explici:tly, this means that there exists a scalar such that ). If then by setting we have (this equality holds no matter w,hat the value of is), which shows that (1) is true in this particular case. Sim!ilarly, if then (2) is true because If (for instance, if they are both equal to the zero vector ) then both (1) and (2) are true (by using for both).