Chapter 8:  Systems of Equations and Matrices

Section 8.1:  Systems of Linear Equations:  Gaussian Elimination

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

* Review for Section 8.1

Objective: Graphing lines

Objective: Plotting points in the plane

Objective: X-intercepts

Objective: Y-intercepts

Objective: Solving linear equations

Section 8.2:  Systems of Linear Equations:  Augmented Matrices

Objective: Solving a system of linear equations using an augmented matrix

* Review for Section 8.2

Objective: Systems of Linear Equations: Gaussian Elimination

Section 8.3:  Matrix Arithmetic

Objective: How to add, subtract, and multiply a matrix by a real number

Objective: How to multiply two matrices together

* Review for Section 8.3

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

* Review for Section 8.4

Objective: Systems of Linear Equations: Gaussian Elimination

Objective: Systems of Linear Equations: Augmented Matrices

Objective: Matrix Arithmetic

Objective: Determinants and Cramer's Rule

Section 8.5:   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)

* Review for Section 8.5

Objective: Systems of Linear Equations: Gaussian Elimination

Objective: Systems of Linear Equations: Matrix Inverses

Section 8.6:  Partial Fraction Decomposition

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

* Review for Section 8.6

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

Section 8.7:  Systems of Non-Liner Equations and Inequalities

Objective: Solving a system of non-linear equations graphically

Objective: Solving a system of non-linear equations using substitution

* Review for Section 8.7

Objective: Systems of Linear Equations: Gaussian Elimination

Objective: Linear Functions

Objective: Quadratic Functions

Objective: Circles

Objective: Parabolas

Objective: Ellipses

Objective: Hyperbolas