Chapter 1Systems of Linear Equations and Elementary Operations on Matrices
1.1Systems of Linear Equations
1.2Elementary Operations on Matrices
Exercises 1.2
Chapter 2Determinants
2.1The Determinant of a Matrix
Exercises 2.126
2.2Properties of Determinants26
Exercises 2.2
2.3The Cofactor Expansion of a Determinant
Exercises 2.3
2.4Cramers Rule
Exercises 2.4
Chapter 3Matrices Algebra
3.1Matrices Arithmetic
Exercise 3.1
3.2Special Matrices
Exercises 3.2
3.3The Inverse of a
Exercises 3.3
3.4Partitioned Matrices
Exercises 3.4
3.5Elementary Matrices
Exercises 3.5
3.6The Rank of a Matrix
Exercises 3.6
Chapter 4Structure of Solutions for Systems of Linear Equations
4.1Existence and Uniqueness of Solutions
Exercises 4.1
4.2Vectors and Operations on Vectors
Exercises 4.2
4.3Linear Relation Among Vectors
Exercises 4.3
4.4Rank of a Vector Set
Exercises 4.4
4.5Structure of Solutions for Systems of Linear Equations
Exercises 4.5
4.6Vector Spaces*
Exercises 4.6
Chapter 5Similar Matrices and Quadratic Forms
5.1Eigenvalues and Eigenvectors
Exercises 5.1
5.2Similar Matrices
Exercises 5.2
5.3Diagonalization of Symmetric Matrices
Exercises 5.3
5.4Quadratic Forms*
Exercises 5.4
Answers to Exercises
References