# Matrices and Matrix Solutions - University of Florida

Matrices and Matrix Solutions Solving Equations With Matrices

Fundamental Concepts Types of Matrices

Matrix Types, Continued Matrix Types, Continued

Matrix Transpose Process of interchanging rows and columns Matrix Equality

I. COMMUTATIVE PROPERTY: A+B=B+A II. ASSOCIATIVE PROPERTY:

A + (B+C) = (A + B) + C NOTE: Thus order of operation in addition is not important!

Matrix Multiplication Matrix Multiplication Properties

Representing Equations Using Matrices Solving Equations By Matrix

Inverse Example of Matrix Solution

Inverse of a 2x2 Matrix a b A

c d

1 d b A da bc c a 1

Note: the determinant of A is: A da bc

Steps: 1. Flip the diagonals, 2. Negate the off-diagonals, and

3. Divide by the determinant. 4. Matrix is SINGULAR when determinant = 0, and thus has no inverse. Other Methods of Matrix Solution

Inverse by elementary row transformations Gaussian elimination Others

For large matrices with many zeros, sparse matrix methods can be used Spreadsheet Functions

TRANSPOSE MMULT MINVERSE The trick in Excel is to press

simultaneously

## Recently Viewed Presentations

• PS-29R42 PS-29R42-2C PS-29R42-4C 29 x 42" PS-29R48 PS-29R48-2C PS-29R48-4C 29 x 48" PS-29R60 PS-29R60-2C PS-29R60-4C 29 x 60" Colors & Finishes: Wood Finishes: 06 Cherry, 76 Dark Oak, 79 Walnut, 80 Natural Oak, 112 Medium Oak, 149 Mahogany. Work surfaces...
• Experimentation & Simulation. Draw Bead Test. Usually used for determining the coefficient of friction between steel sheet and a deep drawing tool in order to determine the ideal lubricant for the forming process.
• Vietnam experienced more consequences from risks and were less inclined to take positive actions. Worldwide, there was an increase in consequences and a decrease in positive actions; the top five consequences showed 3- or 4-point increases from the previous year;...
• Learning Objective: To study Chapter 5 of the novel 'It was the first time that the lawyer had been received in that part of his friend's quarters; and he eyed the dingy, windowless structure with curiosity, and gazed round with...
• The geometric analysis of Erbil Citadel urban space with the proposed Circuit Route shows that: In terms of the . length of center lines of its . axies, the Circuit Route is consisted of . short center lines . This...
• Principles of Inclusivity . Acknowledge individuals have unique and particular needs in the learning and work environment. Respect each individual's right to express and present themselves relative to their religion, culture, ethnic background, sexual orientation, gender identity, physical and mental...
• International benchmark for Fluency is about a minute for a computation at age related. [email protected] Give out the analysis sheet. write the strategy Maybe share findings at St M and St P. ... he has to do some extra exploration...
• Essays will be formally constructed with a clear and logical argument. Evaluation and analysis will be explicit throughout the answers Candidates will be able to make regular and explicit use of the correct analytical and/or evaluative language showing knowledge and...