Let S be a subset of Rn What does it mean when we say that S

Let S be a subset of R^n. What does it mean when we say that S is linearly independent? S is a basis. S is closed under both addition and scalar multiplication. Every vector in R^n is a linear combination of vectors in S. The only way to write O as a linear combination of vectors of S is the zero combination (where one takes zero multiples of each vector of S).

Solution

option d is right.

S is linearly independent in R^n means that

a₁s₁+a₂s₂+...a_ns_n=0 for all a₁=0=a₂=...=a_n

_{that is the only way to write 0 as a linear combination of S is the zero combination ( where one takes zero multiples of each vectors of S)}