can anyone tell me if this definition is correct for linearly independent

..

'A subset

*S*of a vector space

*V*is called

*linearly dependent*if there exists a finite number of distinct vectors

**v**1,

**v**2, ...,

**v**

*n*in

*S*and scalars

*a*1,

*a*2, ...,

*a*

*n*, not all zero, such that

i thought

*a*1,

*a*2, ...,

*a*

*n = 0*

??

some sites like

??

*give a different definition!! which one is true? whose word do i take? (Thinking)*

Linear Algebra: The Basics

Linear Algebra: The Basics

thanks!