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 2.4Cramer’s 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
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