SYSTEMS OF LINEAR EQUATIONS AND MATRICES & DETERMINANTS
CHAPTER 1: SYSTEMS OF LINEAR EQUATIONS
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A. LINEAR EQUATIONS IN n VARIABLES
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B. SOLVING A SYSTEM OF A LINEAR EQUATIONS
1. The Elimination Method
2. The Substitution Method
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C. ROW ECHELON FORM
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D. CONSISTENT AND INCONSISTENT SYSTEMS OF EQUATIONS
–The Geometry Behind Equations in Three Variables
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CHAPTER 2: MATRICES
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A. BASIC CONCEPTS
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B. TYPES OF MATRIX
1. Square Matrix
2. Zero Matrix
3. Identity Matrix
4. Diagonal Matrix
5. Scalar Matrix
6. Symmetric Matrix
7. Antisymmetric Matrix
8. Triangular Matrix
9. Communication Matrix
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C. EQUAL MATRICES
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D. OPERATIONS ON MATRICES
1. Matrix Addition
2. Multiplying a Matrix and a Scalar
3. Matrix Multiplication
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E. THE TRANSPOSE OF A MATRIX
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F. THE INVERSE OF A MATRIX
1. Definition
2. Finding the Inverse of an n × n Matrix
–Cryptography
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CHAPTER 3: DETERMINANTS
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A. THE DETERMINANT OF A MATRIX
1. Determinants of 1 × 1 and 2 × 2 Matrices
2. Minors, Cofactors and Cofactor Matrices
3. The Determinant of a 3 × 3 Matrix
a. Finding the determinant with cofactors
b. The rule of Sarrus
4. The Determinant of an n x n Matrix
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B. PROPERTIES OF DETERMINANTS
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C. APPLICATIONS OF DETERMINANTS
1. Finding the Inverse of a Matrix
2. Solving a System of Equations (Cramer’s Rule)
– Solving a System of Equations With Three Variables
3. Finding the Area of a Triangle
4. Lines in the Plane
a. Testing for collinear points
b. Finding the equation of a line
–Data Matrices