| CHAPTER Ⅰ DETERMINANTS Determinants of Order 2 and 3 1.1 Determinants of order 2 1.2 Determinants of order 3 1.3 Exercises Determinants of Order n 2.1" Defining by numbers of inverted sequence 2.2 Defining by induction 2.3 Exercises Properties of Determinants 3.1 Properties of determinants 3.2 Examples 3.3 Exercises Cramer' s Rule 4.1 Background 4.2 Cramer's rule 4.3 Exercises CHAPTER Ⅱ MATRICES Definition of Matrices 1.1 Definition of a matrix 1.2 Determinant of a square matrix 1.3 Transpose of a matrix 1.4 Exercises Addition and Multiplication by a Number 2.1 Addition of matrices 2.2 Multiplication of a matrix by a number 2.3 Calculation rules 2.4 Exercises 3 Multiplication of Matrices 3.1 Definition of multiplication 3.2 Calculation rules 3.3 Unit matrix 3.4 Powers of square matrices 3.5 Exercises 4 Inverse of a Matrix 4.1 Inverse of a matrix of order 2 4.2 Inverse of an n x n matrix 4.3 Properties of inverse matrices 4.4 Exercises 5 Elementary Operations of a Matrix 5.1 Definition of elementary operations 5.2 Standard form of a matrix 5.3 Elementary square matrix 5.4 Find inverse matrices by elementary operations ~ 5.5 Exercises 6 Rank of a Matrix 6.1 Subdeterminants of a matrix 6.2 Definition of rank of a matrix 6.3 Rank and elementary operations 6.4 Examples 6.5 Exercises 7 Elementary Operations and Elimination 7.1 Representation of equations by matrices 7.2 Elimination in simple cases 7.3 The general case of elimination …… CHAPTER Ⅲ VECTORS CHAPTER Ⅳ STRUCTURE OF SOLUTIONS FOR EQUATIONS CHAPTER Ⅴ EIGENVALUES ANSWERS TO EXERCISES INDEX REFERENCES |
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