Matrices and linear systems, determinants, vector spaces, linear independence, basis and dimension, change of basis, linear transformations,similarity, inner product spaces, eigenvalues and eigenvectors, and diagonalization. Applications of these concepts will also be considered.
Course Learning Outcomes
The student will:
Be able to solve systems of linear equations using multiple methods, including Gaussian elimination and matrix inversion.
Be able to carry out matrix operations, including inverses and determinants.
Demonstrate understanding of the concepts of vector space and subspace.
Demonstrate understanding of linear independence, span, and basis.
Be able to determine eigenvalues and eigenvectors and solve problems involving eigenvalues.
Apply principles of matrix algebra to linear transformations.
Demonstrate application of inner products and associated norms.
Construct proofs using definitions and basic theorems.
College level readiness in reading and writing
Lay, Lay, McDonald; Linear Algebra and its Applications, 5th ed.; Pearson
ISBN Number for Hard Copies of Required MyMathLab Access Codes: 9780321199911
Optional Hard Copy of Text: 9780321982384
Optional Hard Copy of Text with MyMathLab Access: 9780134022697
Calculators may be required for some assignments/assessments at the discrection of the Instructor. Refer to class syllabus for details.
Neither cell phones nor PDA’s can be used as calculators. Calculators may be cleared before tests.
Chapter 1. Linear Equations in Linear Algebra
1.1 Systems of Linear Equations
1.2 Row Reduction and Echelon Forms
1.3 Vector Equations
1.4 The Matrix Equation Ax = b
1.5 Solution Sets of Linear Equations
1.7 Linear Independence
1.8 Introduction to Linear Transformations
1.9 The Matrix of a Linear Transformation
Chapter 2. Matrix Algebra
2.1 Matrix Operations
2.2 The Inverse of a Matrix
2.3 Characterizations of Invertible Matrices
2.5 Matrix Factorizations
Chapter 3. Determinants
3.1 Introduction to Determinants
3.2 Properties of Determinants
3.3 Cramer's Rule, Volume and Linear Transformations
Chapter 4. Vector Spaces
4.1 Vector Spaces and Subspaces
4.2 Null Spaces, Column Spaces and Linear Transformations
4.3 Linearly Independent Sets; Bases
4.5 The Dimension of a Vector Space
4.7 Change of Basis
Chapter 5. Eigenvalues and Eigenvectors
5.1 Eigenvectors and Eigenvalues
5.2 The Characteristic Equation
Chapter 6. Orthogonality and Least Squares
6.1 Inner Product, Length and Orthogonality
6.2 Orthogonal Sets