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- Apply kernel and range to linear transformations.
- Define linear transformations, the geometry of linear operators, and the invertibility of linear transformations.
- Describe matrices as transformations.
General Vector Spaces
- Define vector spaces and subspaces.
- Analyze the relationship of linear independence and vector spaces.
Systems of Linear Equations
- Apply linear systems.
- Explain systems of linear equations.
- Solve linear systems by row reduction.
Matrices and Matrix Algebra
- Describe operations on matrices.
- Demonstrate inverses of matrices.
- Perform matrix factorizations.
- Explain geometry and algebra of vectors.
- Identify dot products.
- Describe vector equations of lines and planes.
- Explain the properties of determinants.
- Apply Cramer’s rule in calculating determinants.
- Identify eigenvalues and eigenvectors.
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