King Abdulaziz University Math 241 Syllabus Department of Mathematics
First Semester 2013-2014 First Semester 1434-1435
Textbook : Elementary Linear Algebra, Sixth Edition (2010) Authors : R. Larson and D.C. Falvo
Chapter Title Section
Title Subtitle
ExamplesHW HW
on line
Weeks
Cha p ter 1 Sy stems of Linear Equ a ti ons
1.1 Introduction to Systems of Linear
Equations
Linear Equations in n Variables, Systems of Linear Equations, Solving a
System of Linear Equations
1-5
Exc. 1-6 16, 65 ,69 ,70 2nd
week 1.2
Gaussian Elimination and
Gauss-Jordan Elimination.
Elementary Row Operations, Gauss –Jordan Elimination, Homogeneous Systems of Linear
Equations
1-9 4, 7, 20,21 27, 44, 47, 48,49,57, 61, 62
2
ndweek
Ch a p ter 2 Ma tr ice s
2.1 Operations with
Matrices
Matrix Addition, Scalar Multiplication , Matrix Multiplication, Systems of
Linear Equations, Partitioned Matrices 1-6 1-3, 7-10, 12-15,21-28,37, 38, 40,41,44,49 51-53.
3rd week 2.2
Properties of Matrix Operations
Properties of Matrix Multiplication,
The Transpose of a Matrix 1-10 1, 5, 7, 13,14, 16,17,19-22,
29,30,32,39,55,57- 59,61,65. HW 1
3rd &
4th weeks 2.3
The Inverse of a Matrix
Properties of Inverses, Systems of
Equations, 1, 3-8
Exc.48 2, 4, 5,9,25-27, 33,38, 39,41, 42,49,52,56- 58
4th week
Chapter 3
Determinants
The Determinant of 3.1a Matrix Triangular Matrices 1-4, 6 13,15,19,33, 41-45, 49,51-54,
67-72,74 HW 2 5th
week
Continu e d Chapter 3 Determinan ts
3.2 Evaluation of a Determinant Using
Elementary Operations.
Determinants and Elementary Column
Operations 2-6 15-20, 31-33, 48 5th
week
3.3 Properties of Determinants
Determinants and the Inverse of a Matrix, Determinants and the
Transpose of a Matrix 1-6 3,4, 7-9, 12, 15, 23,25,45,47,
49,50, 64,65, 67,69, 72,73 HW 3 5th & 6th weeks
3.5 Applications of
Determinants.
The Adjoint of a Matrix, Cramer's rule 1-4 2-4, 11,15, 25-27,29,43 6th week
Cha p ter 4 Vector Sp ace s
4.1
Vectors in Rn Vectors in Rn 4-6 13,15, 23,27,28, 47-49 HW 4 7th
week 4.2
Vector Spaces 2-4, 6-8 1, 3, 4, 6, 19-24,29(a,b), 33,34 7th
4.3 Subspaces of Vector Spaces
Subspaces of Rn
1-4, 6, 8 1, 4, 7, 9, 29, 31-35, 41, 44,45 HW 5 8th week
4.4
Spanning Sets and Linear Independence
Spanning Sets, Linear Dependence and
Linear Independence 1-13 2, 7,9,13,15, 18,19,21,27,
31,32, 39, 49,59,65 HW 6 8th & 9th weeks 4.5
Basis and Dimension
The Dimension of a Vector Space 1-12 8-9, 11,16,17,21,25,35, 41, 43,45,49,63,67, 70, 73,79
9th week 4.6
Rank of a Matrix and Systems of Linear Equations
The Null Space of a Matrix, Solution of Systems of Linear Equations, Systems
of Linear Equations with Square Coefficient Matrices
2-9 2,3,7,9,13,15,21,23, 27,29, 35,
66 HW 7 10th
week
4.7 Coordinates and
Change Basis
Coordinate Representation in Rn,
Change of Basis in Rn 1-5 3, 7-10, 13-16 10th
week
Ch a p ter 5 Inn e r Product Sp ace s
5.2 Inner Product
Spaces
Orthogonal Projections in Inner Product Spaces
1-5, 7, 9- 10
6-7, 111, 15, 17-18, 30-34, 39,
67 HW 8 11th
week 5.3
Orthonormal Bases: Gram- Schmidt Process
: Gram-Schmidt Orthonormalization Process
1, 4, 6-7,
9-10 3, 12, 15, 30-33, 52-54 11th week
Cha p ter 6 Linear Transf or matio ns
6.1 Introduction to
Linear Transformations
1-2, 4-6, 9- 10
2, 3, 9,10,15,17, 20,22,23,
32,33,39,53, 68,69,73 HW 9 12th week 6.2
The Kernel and Range of a Linear
Transformation
The Range of a Linear Transformation, One-to-One and Onto Linear Transformations, Isomorphism of
Vector Spaces
1-2, 4-9 1,3,5,9,11,13,17,
22,31,33,49,51,56 12th
week 6.3
Matrices for Linear Transformations
Composite of Linear Transformations, Nonstandard Bases and General Vector
Spaces
1-2, 4 2,4,5, 11,13,15, 48-50,54,55 12th week
Chapter 7 Ei ge n va lu e s an d Ei g e n ve ct o rs
7.1 Eigenvalues andEigenvectors
Eigenspaces, Eigenvalues and Eigenvectors of Linear
Transformations
1-2, 4-5, 7-
8 2,7, 11(a,b),13(a,b),
15,17,19,23,25,63,65 HW
10 13th week
7.2
Diagonalization Diagonalization and Linear
Transformations 3-8 3, 13, 35-36, 13th
week