Period+8-+Applying+Matrices+to+Linear+Systems+Part+B

= __**Solving A System of Two Equations in Two Unknowns (Using the Inverse)**__ =
 * by Katie, Erin, and Dara**

Matrices can be used to solve a system of equations. In order to do this, one must master how to find the inverse of a matrix.

 * ====To better understand the inverse of a matrix, visit the Inverse Page.====

**Linear Equations of Matrices**

 * =====A linear equation of a matrix can be represented by=====
 * =====Ax=b=====
 * =====Where A represents the matrix, x represents the variable(column vector), and b represents the solution(column vector).=====
 * =====What is a column vector? A column vector is a matrix (m x 1 in size) consisting of a single column of m elements.=====

**What is a System of Equations?**

 * =====Two or more equations that contain the same variables.=====

**Steps to Solving a System of Equations using a Matrix:**

 * =====Matrix can be used to find the solution to a system of equations.=====
 * 1) =====Using your knowledge of multiplying a matrix, you can also write the equations you are solving as matrices.=====
 * 2) =====Once this is done, find the inverse of the coefficient matrix.=====
 * 3) =====Multiply both sides of the equation matrix (from step 1) by the inverse matrix (from step 2).=====
 * 4) =====The result of this multiplication is the solution to your equations.=====
 * 5) =====To check your results, the values you obtained in step 4 can be plugged back into the original equations.=====

Finding the inverse of Matrix

 * =====Use the inverse property of matrices=====
 * =====**Ex:** Let=====

Multiply equations by its inverse

 * =====**Ex:**=====

Why can we multiply by the inverse?

 * =====REMEMBER THESE "SINCE" RULES=====
 * =====[[image:Screen_shot_2012-04-02_at_12.19.09_AM.png width="188" height="49" align="left"]]=====


 * =====Remember that "I" denotes the identity matrix (see here!)=====

x=1 y=2
Sites:

http://home.scarlet.be/math/stelsels.htm#Equivalent-systems-o http://rutherglen.science.mq.edu.au/wchen/lnlafolder/lnla.html http://ceee.rice.edu/Books/CS/chapter2/linear46.html (very helpful) http://www.youtube.com/watch?v=PTN8rganLWo (used for equations) http://www.mathplanet.com/education/algebra-2/matrices/using-matrices-when-solving-system-of-equations http://www.khanacademy.org/math/algebra/algebra-matrices/v/matrices-to-solve-a-system-of-equations