MATRICES

Derinition: A Matrix is a rectangular array of variables or constants in horizontal rows and vertical columns enclosed in brackets.

An Element is each value in a matrix; either a number or a constant.

The dimension of a matrix is the number of rows by number of columns of a matrix.

A matrix is named by its dimensions, the number of rows by the number of columns

Equal Matrices - two matrices that have the same dimensions and each element of one matrix is equal to the corresponding element of the other matrix.

Below is an example of an m by 4 matrix since it has m rows and 4 columns

Lecture Videos

Multiplying Matrices
Determinant and Inverses
Finding the Inverse of a Matrix
Solving Systems Using Matrices

POWERPOINT PRESENTATIONS

Source: Virginia Commonwealth University
University

BASIC PROPERTIES OF MATRICES

The following properties are based on the assumption that the operations are defined for the given matrices
Addition Properties
Associative Property:  (A+B)+C=A+(B+C)
Commutative Property: A+B=B+A
Additive Inverse: A+0=0+A
Additive Inverse:A+(-A)=(-A)+A=0

INTERACTIVE PRACTICE QUIZ

• Basic Operations
  
• Inverses
• Matrix Equation and Systems
• Determinants
• Properties of Determinants

MATRIX FORMULAS

TRANSPOSE
The transpose of a matrix is what you get when the rows of  a column is written as the columns of the original matrix or if the column of a matrix is written as the row of the original matrix.

A 2x2 Example

Diagonal Matrix
A diagonal matrix is a square matrix in which all non diagonal entries are zeros. The identity matrix is a special case of a diagonal matrix

Identity Matrix
An identity matrix is a square matrix with all the diagonal entries having a value of 1 and other non diagonal entries with a value of 0

Determinant of a Matrix
2x2 Matrix: The determinant of a 2x2 matrix is the product of the wings subtracted from the product of the diagonals

3x3 Matrix: Is given by the formula below

Scalar Mutliple
The scalar multiple of a matrix is as a result of multiplying all the entries of a matrix by a constant. The matrix is scaled by that number.