True or False and explain why If v1 v2 v3 v4 is a collection

True or False, and explain why? If {v1, v2, v3, v4} is a collection of vectors in R3 then {v1, v2, v3, v4} must be linearly dependent.

Solution

TRUE

Now, if the number of vectors is fewer than the number of entries in each vector(n), then it has to be linearly dependent.

If the number of vectors is equal to n, then it could be independent or dependent.

But when we have 4 vectors in R^3, they must be linearly dependent because we only need 3 vectors to describe all of R3.