Matrices

=**Assessed Task(s):**= =** Matrices Unit Test (Criterion A) **=

TYPES OF PROBLEMS YOU WILL NEED TO SOLVE:

 * ===Solve systems of equations by graphing, substitution, or addition, as directed.===
 * ===Solve systems of equations by selecting the most appropriate method.===
 * ===Solve applied problems, including coin problems, combining rates, supply and demand, and mixture problems.===
 * ===Know the relationship between a system of equations and a corresponding matrix===
 * ===Perform elementary row operations on a given matrix.===
 * ===Solve systems of equations by the Gauss-Jordan method.===
 * ===Carry out matrix operations, including finding the inverse of a given matrix.===
 * ===Solve a system of equations using the inverse matrix method.===
 * ===Solve a system of inequalities.===
 * ===Decide whether a given point is a feasible solution for a set of constraints.===
 * ===Decide whether a given point is a corner point for a set of constraints.===
 * ===Find the corner points for a set of feasible solutions.===
 * ===Maximize or minimize an objective function subject to a set of constraints.===
 * ===Solve applied problems using a linear programming model.===

Video:

 * Solving linear equations using graphing** (time: 3:57)
 * Solving linear equations using substitution** (time: 8:11)
 * Solving linear equations using addition** (time: 9:59)

Reference Topic Sites:

 * This site gives a nice review of solving simple systems of equations.**
 * @http://www.purplemath.com/modules/systlin1.htm**


 * This site gives a review of solving simple systems of equations by adding with links to solving simple systems using other methods. This is a great site if you take this link along with the other links provided at this site.**
 * @http://www.analyzemath.com/Tutorial-System-Equations/Tutorial-System-Equations.html**

**Reviews translating word problems into systems of equations.** **@http://www.purplemath.com/modules/systprob.htm**


 * Use the calculator on this site to solve the system of equations that you obtain from the word problems in this section.**
 * @http://www.analyzemath.com/Calculators/Calculator_syst_eq.html**

Matrix Solution of a System of Equations
**Gauss:** **@http://www-history.mcs.st-and.ac.uk/~history/Mathematicians/Gauss.html**



**Jordan:** **@http://www-history.mcs.st-and.ac.uk/~history/Mathematicians/Jordan.html**

Video:

 * Solving Systems Using Matrices** (time: 9:58)

Reference Topic Sites:

 * This site gives a Gauss-Jordan Elimination Program:**
 * http://www.nevada.edu/~jfm/finite/inverse/gaussian.htm#top**

**This site is for the TI-83 graphics calculator but it applies to a wide range of calculator models:** **@http://www.wvup.edu/cbrady/GaussJordan.pdf**

Inverse Matrices
**Cayley:** **@http://www-history.mcs.st-and.ac.uk/~history/Mathematicians/Cayley.html**



**Sylvester:** **@http://www-history.mcs.st-and.ac.uk/~history/Mathematicians/Sylvester.html**

Video:

 * Solving Systems of Equations Using Inverses (two variables) ** (time: 6:27)

Reference Topic Sites:

 * Matrix multiplication site:**
 * @http://people.hofstra.edu/faculty/Stefan_Waner/RealWorld/tutorialsf1/frames3_2.html**


 * Interactive site discussing matrix addition:**
 * @http://people.hofstra.edu/faculty/Stefan_Waner/RealWorld/tutorialsf1/frames3_1.html**


 * Interactive matrix multiplication site:**
 * @http://www.cogs.indiana.edu/software/linalg/vectorMatrix/**


 * Interactive site discussing inverse matrices:**
 * @http://people.hofstra.edu/faculty/Stefan_Waner/RealWorld/tutorialsf1/frames3_3.html**

Video:

 * Graphing Systems of Linear Inequalities** (time: 5:16)
 * Linear Programming** (time: 11:10)

Reference Topic Sites:

 * An overview of linear programming:**


 * @http://people.hofstra.edu/faculty/Stefan_Waner/RealWorld/Summary4.html**