View by Category

The presentation will start after a short

(15 second) video ad from one of our sponsors.

Hot tip: Video ads won’t appear to registered users who are logged in. And it’s free to register and free to log in!

(15 second) video ad from one of our sponsors.

Hot tip: Video ads won’t appear to registered users who are logged in. And it’s free to register and free to log in!

Loading...

PPT – DETERMINANTS, INVERSE OF A MATRIX PowerPoint presentation | free to view

The Adobe Flash plugin is needed to view this content

About This Presentation

Write a Comment

User Comments (0)

Transcript and Presenter's Notes

- DETERMINANTS, INVERSE OF A MATRIX
- Reference Croft Davision, Chapter 7, Blocks

3,4 - http//www.math.utep.edu/sos/math
- Determinant
- All square matrices, A, possess a determinant

denoted by - det(A), A.
- Determinant of a 2x2 matrix

If , then

det(A) A ad - bc

A matrix which has a zero determinant is called

singular. Minors and cofactors of a 3x3

matrix Let aij be an element of a matrix A. The

minor of aij is the determinant formed by

crossing out the ith row and jth column of

det(A). The cofactor of aij (-1)ij x (minor

of aij) Note that the term (-1)ij is called the

place sign of the element on the ith row and jth

column. The following may help you to memorize

this.

Determinant of a 3x3 matrix Consider a general

3x3 matrix, A Det(A) can be calculated by

expanding along any row or column. For example,

expanding along the first row

A a11x(its cofactor) a12x(its cofactor)

a13x(its cofactor)

e.g.1 Find the value of and

- Properties of determinants
- i. If every element of a given row (or column)

of the square matrix is multiplied by the same

factor, the value of the determinant is

multiplied by that factor - ii. If B is obtained by interchanged any 2

rows (or columns) of A, then - B -A
- Adding or subtracting a multiple of one row (or

column) to another row (or column) leaves the

determinant unchanged. - iv. If A and B are 2 square matrices and that AB

exists, then det(AB) det(A)det(B).

v. If 2 rows or 2 columns of a square matrix are

equal, the determinant of the matrix is

zero. Exercise p.390 Q1a, 4, 5

Inverse of a Matrix The inverse matrix of a

square matrix A, usually denoted by A-1, has the

property AA-1 A-1A I Note that if

A 0, A does not have an inverse. A ? 0, A

does have an inverse

Finding the inverse of a matrix The followings

are steps to find the inverse of a matrix A when

A ? 0, i. Find the transpose of A, denoted

AT. ii. Replace each element of AT by its

cofactor. The resulting matrix is called the

adjoint of A, denoted adj(A). iii. e.g. 2

Find the inverse of

Application of matrices in computer graphic

(Brief Introduction) Matrices can be used to

represent points, lines and even figures

(graphics). In a 2 dimensional space

represents a point with coordinates

(x0, y0),

represents a straight line with end points (x0,

y0) and (x1, y1)

Similarly can be used to

represent the following figure.

Now, you have seen how graphics can be stored

as matrices. Once a graphic is represented by a

matrix, they can be easily inputted into computer

for storage and manipulation. Manipulation

(include scaling, rotation, reflectionetc.) on

the figure can now be treated as a mathematical

process on the matrices (transformation) which

can be done (easily and fast) by a

computer. However, the details of transforming a

graphical matrix is out of our scope and will not

be discussed here.

Exercise p.398 Q2, 3e,10a, 11a

About PowerShow.com

PowerShow.com is a leading presentation/slideshow sharing website. Whether your application is business, how-to, education, medicine, school, church, sales, marketing, online training or just for fun, PowerShow.com is a great resource. And, best of all, most of its cool features are free and easy to use.

You can use PowerShow.com to find and download example online PowerPoint ppt presentations on just about any topic you can imagine so you can learn how to improve your own slides and presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

You can use PowerShow.com to find and download example online PowerPoint ppt presentations on just about any topic you can imagine so you can learn how to improve your own slides and presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

Recommended

«

/ »

Page of

«

/ »

Promoted Presentations

Related Presentations

Page of

Page of

CrystalGraphics Sales Tel: (800) 394-0700 x 1 or Send an email

Home About Us Terms and Conditions Privacy Policy Contact Us Send Us Feedback

Copyright 2015 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

Copyright 2015 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

The PowerPoint PPT presentation: "DETERMINANTS, INVERSE OF A MATRIX" is the property of its rightful owner.

Do you have PowerPoint slides to share? If so, share your PPT presentation slides online with PowerShow.com. It's FREE!