Linear Algebra for Team-Based Inquiry Learning: 2023 Edition

Learning Outcomes

1. 🔗

   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.
2. 🔗

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

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

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

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

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

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