  A Precalculus Outline

 Chapter 8:  Systems of Equations and Matrices Objective: Systems of Equations and Matrices Objective: Understanding what it means for a point to be a solution to a system of linear equations Objective: Classifying a system of linear equations as consistent or inconsistent Objective: Classifying a system of linear equations is dependent or independent Objective: Solving a system of linear equations by graphing Objective: Solving a system of linear equations using substitution Objective: Solving a consistent independent system of linear equations by elimination Objective: Solving a consistent dependent system of linear equations by elimination Objective: Solving a system of linear equation by elimination and an application Objective: Solving "mixture" problems Objective: Graphing lines Objective: Plotting points in the plane Objective: X-intercepts Objective: Y-intercepts Objective: Solving linear equations Objective: Solving a system of linear equations using an augmented matrix Objective: Systems of Linear Equations: Gaussian Elimination Objective: How to add, subtract, and multiply a matrix by a real number Objective: How to multiply two matrices together Objective: Properties of real number arithmetic Section 8.4: Systems of Linear Equations:  Matrix Inverses Objective: Finding the inverse of a matrix using Gauss-Jordan Elimination Objective: Solving a system of linear equations using a matrix inverse Objective: Systems of Linear Equations: Gaussian Elimination Objective: Systems of Linear Equations: Augmented Matrices Objective: Matrix Arithmetic Objective: Determinants and Cramer's Rule Objective: Finding the determinant of a 2 x 2 matrix Objective: Finding the determinant of a 3 x 3 matrix Objective: Finding the determinant of a 4 x 4 matrix Objective: Solving a system of linear equations using Cramer's Rule Objective: Finding the inverse of a matrix using determinants (co-factors) Objective: Systems of Linear Equations: Gaussian Elimination Objective: Systems of Linear Equations: Matrix Inverses Objective: Finding a partial fraction decomposition of a rational expression with distinct linear factors Objective: Finding a partial fraction decomposition of a rational expression with repeated linear factors Objective: Finding a partial fraction decomposition of a rational expression with an irreducible quadratic factor Objective: Finding a partial fraction decomposition of a rational expression where long division is required first Objective: Overview of factoring polynomials Objective: Factoring out greatest common factor part 1 Objective: Factoring out greatest common factor part 2 Objective: Factoring out greatest common factor part 3 Objective: Factoring out greatest common factor part 4 Objective: Difference of squares part 1 Objective: Difference of squares part 2 Objective: Difference of squares part 3 Objective: Factoring trinomials part 1 Objective: Factoring trinomials part 2 Objective: Factoring trinomials part 3 Objective: Factoring trinomials part 4 Objective: Factoring trinomials part 5 Objective: Factoring trinomials Objective: How to perform polynomial long division Objective: Solving a system of non-linear equations graphically Objective: Solving a system of non-linear equations using substitution Objective: Systems of Linear Equations: Gaussian Elimination Objective: Linear Functions Objective: Quadratic Functions Objective: Circles Objective: Parabolas Objective: Ellipses Objective: Hyperbolas