mth360 | undergraduate
This course provides a survey of the concepts related to linear algebra. Students examine the geometry of vectors, matrices, and linear equations, including Gauss-Jordan elimination. Students explore the concepts of linear independence, rank, and linear transformations. Vector spaces, bases, and change of bases are discussed, including orthogonality and the Gram–Schmidt process. In addition, students investigate determinants, eigenvalues, and eigenvectors.
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Determinants, Orthogonality, Eigenvalues, and Eigenvectors
- Decompose a vector space into its subspace and orthogonal complement.
- Evaluate eigenvalues and eigenvectors using the characteristic polynomial.
- Calculate determinants.
- Calculate the dot, or inner, product of two vectors.
- Examine applications of linear algebra using Leontief’s closed model.
- Review linear algebra topics.
Vectors and Linear Transformations
- Transform vectors in two- and three-dimensional spaces using matrices.
- Use linear transformations to transform a vector from Rn to Rm.
- Simplify vectors into linear combinations using vector algebra.
- Solve applications of linear systems.
- Determine a spanning set for independent vectors.
Linear Equations and Matrix Algebra
- Solve systems of linear equations with m equations and n unknowns.
- Solve linear equations using Gauss-Jordan elimination.
- Perform matricial calculations.
- Determine the invertibility of a matrix.
- Determine the kernel and range of the matrix representation of a subspace of Rn.
- Determine the basis and dimension of a subspace of Rn.
- Extrapolate abstract vector spaces from specific vector spaces.
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