MATH 2000  Introduction to Linear Algebra Credit Hours: 3.00 Prerequisites: MATH 1760 with grade C or better; or an equivalent college course; or an acceptable score on a placement or prerequisite exam
This course covers systems of linear equations; the algebra of matrices; determinants and their applications; the theory of vector spaces, with emphasis on Euclidean n‑space; linear transformations and their matrix representations; eigenvalues and eigenvectors; similar matrices; symmetric matrices; the spectral theorem, and applications.
Billable Contact Hours: 3
Search for Sections Transfer Possibilities Michigan Transfer Network (MiTransfer)  Utilize this website to easily search how your credits transfer to colleges and universities. OUTCOMES AND OBJECTIVES Outcome 1: Upon completion of this course the student will solve problems, use algorithms and demonstrate comprehension of concepts from: Linear systems of equations and their applications.
Objectives: Students will:
 Solve linear systems by elimination.
 Describe solutions of systems geometrically and algebraically.
 Define and reduce matrices to reduced row echelon form.
 Use Gaussian elimination to solve linear systems by forming an augmented matrix.
 Use GaussJordan elimination to solve homogeneous and non homogeneous systems.
Outcome 2: Upon completion of this course the student will solve problems, use algorithms and demonstrate comprehension of concepts from: Matrices and their operations.
Objectives: Students will:
 Perform matrix operations.
 Work with properties of matrices.
 Calculate the inverse of a matrix by using a formula or by reducing an n x 2n matrix.
 Determine operations using elementary matrices.
 Solve linear system Ax = b by using A^{1} .
Outcome 3: Upon completion of this course the student will solve problems, use algorithms and demonstrate comprehension of concepts from: Determinants and their properties.
Objectives: Students will:
 Evaluate the determinant of a matrix.
 Use the determinant of a matrix to determine whether or not the inverse of the matrix exists.
 Use elementary operations to evaluate determinants.
 Work with the properties of determinants.
 Use Cramer’s rule and determinants to solve systems of linear equations of the form Ax = b, A not equal to 0.
Outcome 4: Upon completion of this course the student will solve problems, use algorithms and demonstrate comprehension of concepts from: Vector spaces.
Objectives: Students will:
 Test sets for the axioms of a vector space.
 Establish a list of vector properties
 Test a subset for a subspace of a vector space.
 Test a solution vector of a homogeneous system to be a subspace of R^{n}
 Define a linear combination of vectors v_{1}, v_{2},…v_{n}.
 Test for spaces that are spanned by vectors.
 Test for linearly independent and linearly dependent sets.
 Determine whether a set is a basis for R^{n}
 Test for bases of a vector space.
 Determine the dimension of a vector space and a solution space.
 Find bases for a row space, column space, null space, and left null space.
Outcome 5: Upon completion of this course the student will solve problems, use algorithms and demonstrate comprehension of concepts from: Inner product spaces.
Objectives: Students will:
 Define the Euclidean inner product on R^{2}, R^{3} and R^{n}
 Define the length and distance in an inner product space.
 Define the norm in R^{n}
 Calculate an angle in the inner product space.
 Establish the orthogonality of a set in an inner product space.
 Use the GramSchmidt process to find orthonormal bases for the inner product space.
 Test for linear independence of orthogonal sets in the inner product space.
 Find the coordinates of a vector v relative to orthonormal bases, and express v in terms of orthonormal bases.
 Define orthogonal matrices.
Outcome 6: Upon completion of this course the student will solve problems, use algorithms and demonstrate comprehension of concepts from: Eigenvalues and eigenvectors of a matrix.
Objectives: Students will:
 Find the eigenvalues and eigenvectors of a matrix.
 Find the eigenvalues and eigenvectors of powers of a matrix.
 Test for diagonalizable matrices.
 Define similar matrices.
 Discuss the properties of a similar matrix.
 Compute powers of a matrix.
 Discuss orthogonal diagonalization of a symmetric matrix.
 Use the eigenvalues and eigenvectors to express a general conic in standard form; find the angle of rotation and sketch.
Outcome 7: Upon completion of this course the student will solve problems, use algorithms and demonstrate comprehension of concepts from: Linear Transformations.
Objectives: Students will:
 Define Linear Transformation T: V –> W
 Discuss zero and identity transformations
 Determine whether or not a transformation is linear
 Find the standard matrix of a linear transformation
 Find the Kernel and range of a linear transformation
 Determine the rank and nullity of a linear transformation
 Find a change of basis
 Find nonstandard matrices of a linear transformation
 Find matrices of sums, products, compositions, and inverses of linear transformations.
COMMON DEGREE OUTCOMES (CDO)
 Communication: The graduate can communicate effectively for the intended purpose and audience.
 Critical Thinking: The graduate can make informed decisions after analyzing information or evidence related to the issue.
 Global Literacy: The graduate can analyze human behavior or experiences through cultural, social, political, or economic perspectives.
 Information Literacy: The graduate can responsibly use information gathered from a variety of formats in order to complete a task.
 Quantitative Reasoning: The graduate can apply quantitative methods or evidence to solve problems or make judgments.
 Scientific Literacy: The graduate can produce or interpret scientific information presented in a variety of formats.
CDO marked YES apply to this course: Critical Thinking: YES Quantitative Reasoning: YES COURSE CONTENT OUTLINE
 Systems of Linear Equations
 Introduction to Systems of Linear Equations
 Gaussian Elimination and GaussJordan Elimination
 Solving Systems of Homogeneous Linear Equations
 Solve Applications
 Matrices
 Operations with Matrices
 Properties of Matrix Operations
 The Inverse of a Matrix
 Elementary Matrices
 Solve Systems by Using Inverse Matrices
 Determinants
 The Determinant of a Matrix
 Evaluation of a Determinant Using Elementary Operations
 Properties of Determinants
 Solve Systems by Using Cramer’s Rule
 Use Determinants to find the Inverse of a Matrix
 Vector space
 Vectors in Plane End Space
 Subspaces of Vector Spaces
 Spanning Sets and Linear Independence
 Basis and Dimension
 Rank of a Matrix and Systems of Linear Equations
 Coordinates and Change of Basis
 Applications of Vector Spaces
 Inner Product Spaces
 Length and Dot Product in Rn
 Inner Product Spaces
 Orthonormal Bases: GramSchmidt Process
 Applications of Inner Product Spaces
 Eigenvalues and Eigenvectors
 Eigenvalues and Eigenvectors
 Diagonalization
 Symmetric Matrices and Orthogonal Diagonalization
 Use Eigenvalues and Eigenvectors to Rotate Axis and Sketch General Conic Sections
 Linear Transformations
 Introduction to Linear Transformations
 The Kernel and Range of a Linear Transformation
 Standard and NonStandard matrices for Linear Transformations
 Transition Matrices
 Applications of Linear Transformations
Primary Faculty Friday, David Secondary Faculty Williams, Paul Associate Dean McMillen, Lisa Dean Pritchett, Marie
Primary Syllabus  Macomb Community College, 14500 E 12 Mile Road, Warren, MI 48088
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