The image contains guidelines on how to prepare for questions related to subspaces and vector spaces. Here's a breakdown of the key concepts:

1. Subspaces: Be familiar with the definitions of subspaces, how to determine whether a subset of a vector space is a subspace or not.
2. Linear Independence and Basis: Understand these concepts, as they are foundational in determining subspaces.
3. Coordinates: You should know how to work with coordinates within a vector space or subspace.
4. Vector Spaces: The concept of vector spaces isn't limited to $\mathbb{R}^n$ but also applies to other structures like polynomials and matrices.
5. Linear Dependence in General Spaces: Grasp the idea that linear dependence and coordinate concepts also apply to spaces of polynomials and matrices.

Would you like more detailed explanations on any of these topics?

Here are 5 follow-up questions to expand on this information:

1. How can you prove that a subset is a subspace of a vector space?
2. What are the three main properties that a subspace must satisfy?
3. Can you explain the relationship between linear independence and the basis of a vector space?
4. How do coordinates work in spaces beyond $\mathbb{R}^n$, such as in polynomial spaces?
5. What is an example of a vector space of matrices, and how do linear dependence concepts apply there?

Tip: When showing that a subset is a subspace, always verify closure under addition and scalar multiplication, along with checking if the zero vector is included.