COLLEGE ALGEBRA
Chapter 6 MAXTRIX SOLUTIONS TO
LINEAR SYSTEMS Section: 6.1 – 6.6 Outcomes: The student will solve simple linear systems using inverse matrices and determinants. 

A  B  C  D  F  N  Specific Competencies Demonstrate the ability to: 

6.1  Write the augmented matrix for a linear system.  
6.1  Perform matrix row operations.  
6.1  Use matrices and Gaussian elimination to solve systems.  
6.1  Use matrices and GaussJordan elimination to solve systems.  
6.2  Apply Gaussian elimination to systems without unique solutions.  
6.2  Apply Gaussian elimination to systems with more variables than equations.  
6.2  Solve problems involving systems without unique solutions.  
6.3  Use matrix notation.  
*6.3  Understand what is meant by equal matrices.  
6.3  Add and subtract matrices.  
6.3  Perform scalar multiplication.  
6.3  Solve matrix equations.  
6.3  Multiply matrices.  
*6.3  Describe applied situations with matrix operations.  
6.4  Find the multiplicative inverse of a square matrix.  
6.4  Use inverses to solve matrix equations.  
*6.4  Encode and decode messages.  
6.5  Evaluate a secondorder determinant.  
6.5  Solve a system of linear equations in two variables using Cramer’s rule.  
6.5  Evaluate a thirdorder determinant.  
6.5  Solve a system of linear equations in three variables using Cramer’s rule.  
*6.5  Use determinants to identify
inconsistent systems and systems with dependent equations. 

6.5  Evaluate higherorder determinants. 
Chapter 7 CONIC SECTIONS Section:
7.1 – 7.3 Outcomes: The student will recognize, graph and write equations of conics with center at the origin. 

A  B  C  D  F  N  Specific Competencies Demonstrate the ability to: 

*7.1  Graph ellipses centered at the origin.  
*7.1  Write equations of ellipses in standard form.  
*7.1  Graph ellipses not centered at the origin.  
*7.1  Solve applied problems involving ellipses.  
*7.2  Locate a hyperbola’s vertices and foci.  
*7.2  Write equations of hyperbolas in standard form.  
*7.2  Graph hyperbolas centered at the origin.  
*7.2  Graph hyperbolas not centered at the origin.  
*7.2  Solve applied problems involving hyperbolas.  
7.3  Graph parabolas with vertices at the origin.  
7.3  Write equations of parabolas in standard form.  
7.3  Graph parabolas with vertices not at the origin.  
*7.3  Solve applied problems involving parabolas. 