Mark each statement True or False and justify each answer?

a. Two vectors are linearly dependent if and only if they lie on a line through the origin.


b. if a set contains fewer vectors than there are entries in the vectors, then the set is linearly independent


c. If x and y are linearly indepedent, and if z is in Span{x,y},, then {x,y,z} is linearly independent


d. If a set in R^n is linearly dependent, then the set contains more vectors than there are entries in each vector.Mark each statement True or False and justify each answer?
a) False, they have to be on the same line, but the line don't have to go through the origin





b) False, the vectors can be multiples of each other and be dependent





c) False, (x,y,z) is linearly dependent,as z = ax + by





d) False, the set can thus be two vectors, multiples of each other





THEY ARE ALL FALSE !!!