Question

(a) If is a linearly dependent set of vectors in Rn

, show that is

also linearly dependent, where X4 is any other vector in Rn

.

(b) Prove that any set which contains a linearly dependent set is linearly dependent.​

Answer 1

Answer:you can take the vectors to form a matrix and check its determinant. If the determinant is non zero, then the vectors are linearly independent. Otherwise, they are linearly dependent.

Step-by-step explanation:I think you're supposed to show this by contradiction, but not sure how.

I tried:

Let V be a linearly independent set of vectors {v1,...vn} such that a1v1+...+anvn=0 and a1=...=an=0. Then, V is a subset of {v1,...,vn+1} and a1v1+...+an+1vn+1=0 where a1=...=an+1=0. Therefore, the set {v1,...,vn+1} is again linearly independent.