State whether the following argument is valid or not and exp

State whether the following argument is valid or not, and explain. \\The

properties of a vector space yield that the scalar 0 times any vector is

the zero vector. So 0v1+ 0v2+ 0v3=0

. Since the coecients are all 0, the vectors v1,v2, and v3

are linearly independent.\"

Solution

NO for linear indepence,

a1v1+a2v2+a3v3=0

must imply all a1,a2,a3 to be zero only then they are independent , the converse is not true.