Let x1, x2,..., xk be linearly independent vectors in a vector space V. (a) If we add

Question:

Let x1, x2,..., xk be linearly independent vectors in a vector space V.
(a) If we add a vector xk+1 to the collection, will we still have a linearly independent collection of vectors? Explain.
(b) If we delete a vector, say xk, from the collection, will we still have a linearly independent collection of vectors? Explain.