HOME COURSES PREVIEW REVIEW ABOUT CONTACT
 Toll-Free Info & Ordering M-F: 9am-5pm (PST): (877) RAPID-10
 24/7 Technical Support
 QUICK TOUR
 Member Login:
 Rapid Courses Catalog Mathematics in 24 Hours Chemistry in 24 Hours Biology in 24 Hours Physics in 24 Hours
Math Survival Weekly
Get the insider's tips and tricks in how to survive your math course and ace the next test. Subscribe the Web's only math weekly newsletter for students and learn:
- How to Study Math Effectively
- How to Take Math Courses Strategically
- How to Solve Math Problems Systematically
- How to Score High in Math Exams
- How to Master Math Rapidly

Enter your name and email below and get started today!
 Your Name * Email *
 Math Study Lounge These study sheets are for quick review on the subjects. Refer to our rapid courses for comprehensive review.     - Getting Started with Algebra     - Geometry Basics     - How to Solve Math Problems     - Trigonometry Quick Review     - Statistics At-A-Glance     - Calculus Preview

Matrices

 Topic Review on "Title": Definition of a matrix: Any 2-dimensional array of real or complex numbers. Square matrix: A matrix of type . Diagonal: The entries of a square matrix in the i-th line and i-th column (same index i), for some i. Identity matrix: A square matrix with 1’s on the diagonal and 0’s off the diagonal. Zero matrix: Any matrix (of any type), with only zero entries. Definition of a 2-dimensional matrix: We define of a 2-dimensional matrix as: . Definition of the rank of a matrix: The rank of a matrix A is the greatest n such that A has a square sub-matrix of type nxn with determinant not equal to zero. Definition of an invertible matrix: We say a square matrix A is invertible if there exits a (square) matrix  such that =identity matrix. Cramer’s Rule: If  is a square matrix, then the equation  has a unique solution if and only if and the solution is.

Rapid Study Kit for "Title":
 Flash Movie Flash Game Flash Card Core Concept Tutorial Problem Solving Drill Review Cheat Sheet

 "Title" Tutorial Summary : Linear systems can be solved with the use of matrices. Matrix properties and operations facilitated the arrival to solutions with fewer calculations. Some examples show matrix computations and the nature of their solutions. The idea of Cramer’s rule can be formulated with the use of matrices. Cramer’s rule is a famous rule that uses determinants to finding solutions to a system of equations. The addition or multiplication of rows and columns in a matrix allow matrices to be reduced.

 Tutorial Features: Specific Tutorial Features: • Matrix operations are shown in some of the examples. • Matrix computations are presented in the examples. • Step by step explanation of the rank of a matrix with respect to a determinant is shown in a couple of examples. Series Features: • Concept map showing inter-connections of new concepts in this tutorial and those previously introduced. • Definition slides introduce terms as they are needed. • Visual representation of concepts • Animated examples—worked out step by step • A concise summary is given at the conclusion of the tutorial.

 "Title" Topic List: The definition of matricesMatrices The sum and product of matrices Determinants Matrices that are two dimensional Matrices that are three dimensionalA rank of a matrixLinear systems and the rank of a matrixMatrix Inverse Definition of the inverse of a matrixCramer’s RuleMatrix Reduction Definition of equivalent matrices

See all 24 lessons in High School Algebra 2, including concept tutorials, problem drills and cheat sheets: Teach Yourself High School Algebra 2 Visually in 24 Hours

 ©2014 Rapid Learning Center. Privacy Policy | Disclaimer Chemistry Survival Publishing, Biology Survival Publishing and Physics Survival Publishing are the divisions of Rapid Learning Inc.