Home Site Map Contact Us
Rapid Learning Member Login  
Rapid Learning Blog Rapid Learning on Facebook Rapid Learning on Youtube Rapid Learning on Twitter
 How to Learn in 24 Hours?

 Need Help?
M-F: 9am-5pm(PST):
Toll-Free: (877) RAPID-10
or 1-877-727-4310

24/7 Online Technical Support:
The Rapid Support Center
vip@rapidlearningcenter.com

Secure Online Order:
Buy Now

 

 Got Questions?
Frequently Asked Questions
 Need Proof?
Testimonials by Our Users

Trustlink is a Better Business Bureau Program.
Rapid Learning Center is a fivr-star business.

External TrustLink Reviews




 Member Login:
User ID: 
Password: 
 

 Rapid Learning Courses:

MCAT in 24 Hours (2021-22)

USMLE in 24 Hours (Boards)

Chemistry in 24 Hours

Biology in 24 Hours

Physics in 24 Hours

Mathematics in 24 Hours

Psychology in 24 Hours

SAT in 24 Hours

ACT in 24 Hours

AP in 24 Hours

CLEP in 24 Hours

DAT in 24 Hours (Dental)

OAT in 24 Hours (Optometry)

PCAT in 24 Hours (Pharmacy)

Nursing Entrance Exams

Certification in 24 Hours

eBook - Survival Kits

Audiobooks (MP3)


 Tell-A-Friend:
Have friends taking science and math courses too? Tell them about our rapid learning system.



Matrices and Determinants

Topic Review on "Title":

Definition of a matrix:

  • Any 2-dimensional array of real or complex numbers.  

Square matrix:

  • A matrix of type nxn.

 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 B such that AB=BA=identity matrix.

Cramer’s Rule:

  • If A is a square matrix, then the equation AV=w has a unique solution if and only if and the solution is then .

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

"Title" Tutorial Summary :

Matrices are important tools in solving linear systems. Their properties and operations allow solutions to be arrived at in fewer steps than other traditional approaches to algebra problems. Performing computations with matrices is shown in this tutorial through the examples.

Determinants are used introduced so the idea of Cramer’s rule can be formulated. Cramer’s rule is a famous rule that uses determinants to finding solutions to a system of equations. Reducing matrices involving the addition or multiplication of rows and columns in a matrix


Tutorial Features:

Specific Tutorial Features:

• The operations of matrices are shown in some of the examples.
• Performing computation with matrices is 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:
Definition of matrices
Matrices
Sums and products of matrices
Determinants
2 Dimensional Matrices
3 Dimensional Matrices
Definition of a rank of a matrix
Application to linear systems
The Inverse of a Matrix
Definition of the inverse of a matrix
Cramer’s Rule
Reduction of matrices
Definition of equivalent matrices


See all 24 lessons in Pre-Calculus, including concept tutorials, problem drills and cheat sheets:
Teach Yourself Pre-Calculus Visually in 24 Hours

© 2021 Rapid Learning Inc. All rights reserved         Disclaimer | Privacy Policy