Linear Algebra for Team-Based Inquiry Learning: 2023 Edition PREVIEW

Learning Outcomes

1. Explain why a given set with defined addition and scalar multiplication does satisfy a given vector space property, but nonetheless isn't a vector space.

2. Determine if a Euclidean vector can be written as a linear combination of a given set of Euclidean vectors by solving an appropriate vector equation.

3. Determine if a set of Euclidean vectors spans ${\mathbb{R}}^n$ by solving appropriate vector equations.

4. Determine if a subset of ${\mathbb{R}}^n$ is a subspace or not.

5. Determine if a set of Euclidean vectors is linearly dependent or independent by solving an appropriate vector equation.

6. Explain why a set of Euclidean vectors is or is not a basis of ${\mathbb{R}}^n\text{.}$

7. Compute a basis for the subspace spanned by a given set of Euclidean vectors, and determine the dimension of the subspace.

8. Answer questions about vector spaces of polynomials or matrices.

9. Find a basis for the solution set of a homogeneous system of equations.