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# STARK STATE COLLEGE GENERAL SYLLABUS

## Course Information

Course Name: Linear Algebra

Course Number: MTH226


<table border=1 style='margin: auto; word-wrap: break-word;'><tr><td colspan="2">Required Materials</td></tr><tr><td rowspan="2">Textbook(s):</td><td style='text-align: center; word-wrap: break-word;'>Elementary Linear Algebra-8th edition; by Ron Larson</td></tr><tr><td style='text-align: center; word-wrap: break-word;'>Cengage Learning 2017;</td></tr><tr><td style='text-align: center; word-wrap: break-word;'>Required Readings:</td><td style='text-align: center; word-wrap: break-word;'>ISBN: 978-1-305-65800-4 (student edition); 978-1-305-95320-8 (loose-leaf edition)</td></tr><tr><td style='text-align: center; word-wrap: break-word;'>Additional Materials:</td><td style='text-align: center; word-wrap: break-word;'>none</td></tr><tr><td style='text-align: center; word-wrap: break-word;'></td><td style='text-align: center; word-wrap: break-word;'>A graphing calculator is recommended but not required.</td></tr></table>

## Course Outline/Calendar

The date of coverage and order of coverage may be modified based on the faculty member and events beyond the control of faculty members that interfere with class times and teaching.


<table border=1 style='margin: auto; word-wrap: break-word;'><tr><td style='text-align: center; word-wrap: break-word;'>Week</td><td style='text-align: center; word-wrap: break-word;'>Chapter/Topic/Lab</td></tr><tr><td style='text-align: center; word-wrap: break-word;'>1</td><td style='text-align: center; word-wrap: break-word;'>Ch. 1 Systems of Linear Equations (Review)
1.1 Introduction to Systems of Linear Equations
1.2 Gaussian and Gauss-Jordan Eliminations
1.3 Applications of Systems of Linear Equations
Ch. 2 Matrices (Review)
2.1 Operations with Matrices
2.2 Properties of Matrix Operations
2.3 The Inverse of a Matrix</td></tr><tr><td style='text-align: center; word-wrap: break-word;'>2</td><td style='text-align: center; word-wrap: break-word;'>2.4 Elementary Matrices
2.6 Some Applications of Matrix Operations
Ch. 3 Determinants (Review)
3.1 The Determinant of a Matrix
3.2 Determinants and Elementary Operations
3.3 Properties of Determinants
3.4 Applications of Determinants</td></tr></table>

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<table border=1 style='margin: auto; word-wrap: break-word;'><tr><td style='text-align: center; word-wrap: break-word;'>Week</td><td style='text-align: center; word-wrap: break-word;'>Chapter/Topic/Lab</td></tr><tr><td style='text-align: center; word-wrap: break-word;'></td><td style='text-align: center; word-wrap: break-word;'>Test #1 (Chapters 1, 2, 3)</td></tr><tr><td style='text-align: center; word-wrap: break-word;'>3</td><td style='text-align: center; word-wrap: break-word;'>Ch. 4 Vector Spaces\n4.1 Vectors in Rn\n4.2 Vector Spaces\n4.3 Subspaces of a Vector Space</td></tr><tr><td style='text-align: center; word-wrap: break-word;'>4</td><td style='text-align: center; word-wrap: break-word;'>44 Spanning Sets and Linear Independence\n4.5 Basis and Dimension\n4.6 Rank of a Matrix and Systems of Linear Equations</td></tr><tr><td style='text-align: center; word-wrap: break-word;'>5</td><td style='text-align: center; word-wrap: break-word;'>4.7 Coordinates and Change of Basis\n4.8 Applications of Vector Spaces</td></tr><tr><td style='text-align: center; word-wrap: break-word;'>6</td><td style='text-align: center; word-wrap: break-word;'>Ch. 5 Inner Product Spaces\n5.1 Length and Dot Product in Rn\n5.2 Inner Product Spaces</td></tr><tr><td style='text-align: center; word-wrap: break-word;'>7</td><td style='text-align: center; word-wrap: break-word;'>5.3 Orthonormal Bases: Gram-Schmidt Process (if time permits)\n5.4 Mathematical Models and Least Square Analysis (if time permits)</td></tr><tr><td style='text-align: center; word-wrap: break-word;'>8</td><td style='text-align: center; word-wrap: break-word;'>5.5 Applications of Inner Product Spaces\nTest #2 (Chapters 4, 5)</td></tr><tr><td style='text-align: center; word-wrap: break-word;'>9</td><td style='text-align: center; word-wrap: break-word;'>Ch. 6 Linear Transformations\n6.1 Introduction to Linear Transformations\n6.2 The Kernel and Range of a Linear Transformation</td></tr><tr><td style='text-align: center; word-wrap: break-word;'>10</td><td style='text-align: center; word-wrap: break-word;'>6.3 Matrices for Linear Transformations\n6.4 Transition Matrices and Similarity</td></tr><tr><td style='text-align: center; word-wrap: break-word;'>11</td><td style='text-align: center; word-wrap: break-word;'>6.5 Applications of Linear Transformations\nCh. 7 Eigenvalues and Eigenvectors\n7.1 Eigenvalues and Eigenvectors</td></tr><tr><td style='text-align: center; word-wrap: break-word;'>12</td><td style='text-align: center; word-wrap: break-word;'>7.2 Diagonalization\n7.3 Symmetric Matrices and Orthogonal Diagonalization</td></tr><tr><td style='text-align: center; word-wrap: break-word;'>13</td><td style='text-align: center; word-wrap: break-word;'>7.4 Applications of Linear Transformations\nCh. 8 Complex Vector Spaces. Abstract Vector Spaces\n8.1 Complex Numbers (review)\n8.2 Conjugates and Division of Complex Numbers (review)</td></tr><tr><td style='text-align: center; word-wrap: break-word;'>14</td><td style='text-align: center; word-wrap: break-word;'>8.3 Polar Form and DeMoivre’s Theorem (review)\n8.4 Complex Vector Spaces and Inner Products.\nAbstract Vector Spaces</td></tr><tr><td style='text-align: center; word-wrap: break-word;'>15</td><td style='text-align: center; word-wrap: break-word;'>Make up week (if time permits)</td></tr><tr><td style='text-align: center; word-wrap: break-word;'>16</td><td style='text-align: center; word-wrap: break-word;'>Final Exam\nTest #3 (Chapters 6, 7, 8)</td></tr></table>