Question

Answer each one, with (brief) justification. Throughout, V denotes a vector space, and bold-face letters like u, v, etc denote vectors in V.

A1. Suppose there are three linearly independent vectors in V. Is V necessarily finite-dimensional?

A2. Suppose there are three vectors in V that span V. Is V necessarily finite-dimensional?

A3. What is the dimension of the vector space of all polynomials of degree 4 or less?

A4. Can an infinite-dimensional vector space contain a finite-dimensional subspace?

A5, In a finite-dimensional vector space, is every spanning set necessarily finite?

A6. Can R³ contain a four-dimensional subspace?

Answer 1