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Nov 24, 2024
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MA 383 - Linear Algebra3 lecture hours 0 lab hours 3 credits
Course Description
Topics include the use of elementary row operations to solve systems of linear equations, linear dependence, linear transformations, matrix operations, inverse of a matrix, determinants, subspaces, spaces, column spaces, dimension and rank, eigenvalues and eigenvectors, diagonalization of matrices, similarity, inner product and orthogonality, orthogonal projections and Gram-Schmidt process. (prereq: MA 231 or MA 225 or MA 3501 )
Course Learning Outcomes
Upon successful completion of this course, the student will be able to:
• Learn the basic theory of linear algebra
• Apply the basic row operations to solve systems of linear equations
• Solve a matrix equation and a vector equation
• Understand the concept of linear dependence and independence
• Understand matrix transformations and linear transformations and the relationship between them
• Perform all matrix operations, be able to find the inverses and determinants of matrices
• Understand the concept of a subspace and basis
• Find the column and null spaces of a matrix and their dimensions, and the rank of a matrix
• Understand the concept of similarity
• Find the eigenvalues and eigenvectors of a matrix
• Understand the concept of inner product and orthogonality, orthogonal and orthonormal bases
• Apply Gram-Schmidt process
Prerequisites by Topic
• Differential and integral calculus
• Basic vector mathematics
Course Topics
• Introduction to systems of linear equation and solving them using matrices, row operations (3 classes)
• Vectors, vector and matrix equations (3 classes)
• Matrix operations (3 classes)
• Vector spaces including bases, dimension, rank and nullity ( 3 classes)
• Linear independence (1 class)
• Matrix transformations, linear transformations and their relations (3 classes)
• Similarity (1 class)
• Eigenvalues, eigenvectors and their applications (3 classes)
• Diagonalization (2 classes)
• Inner product and orthogonality (3 classes)
• Applications (1 class)
• Reviews and exams (4 classes)
Coordinator
Yvonne Yaz
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