View by Category

Loading...

PPT – MATRICES PowerPoint presentation | free to download - id: 1ff55d-MjBlN

The Adobe Flash plugin is needed to view this content

About This Presentation

Write a Comment

User Comments (0)

Transcript and Presenter's Notes

MATRICES

- MATRIX OPERATIONS

About Matrices

- A matrix is a rectangular arrangement of numbers

in rows and columns. Rows run horizontally and

columns run vertically. - The dimensions of a matrix are stated m x n

where m is the number of rows and n is the

number of columns.

Equal Matrices

- Two matrices are considered equal if they have

the same number of rows and columns (the same

dimensions) AND all their corresponding elements

are exactly the same.

Special Matrices

- Some matrices have special names because of what

they look like. - Row matrix only has 1 row.
- Column matrix only has 1 column.
- Square matrix has the same number of rows and

columns. - Zero matrix contains all zeros.

Matrix Addition

- You can add or subtract matrices if they have the

same dimensions (same number of rows and

columns). - To do this, you add (or subtract) the

corresponding numbers (numbers in the same

positions).

Matrix Addition

Example

Scalar Multiplication

- To do this, multiply each entry in the matrix by

the number outside (called the scalar). This is

like distributing a number to a polynomial.

Scalar Multiplication

Example

Matrix Multiplication

- Matrix Multiplication is NOT Commutative! Order

matters! - You can multiply matrices only if the number of

columns in the first matrix equals the number of

rows in the second matrix.

Matrix Multiplication

- Take the numbers in the first row of matrix 1.

Multiply each number by its corresponding number

in the first column of matrix 2. Total these

products.

The result, 11, goes in row 1, column 1 of the

answer. Repeat with row 1, column 2 row 1

column 3 row 2, column 1 ...

Matrix Multiplication

- Notice the dimensions of the matrices and their

product.

3 x 2

2 x 3

3 x 3

__

__

__

__

Matrix Multiplication

- Another example

3 x 2

2 x 1

3 x 1

Matrix Determinants

- A Determinant is a real number associated with a

matrix. Only SQUARE matrices have a determinant. - The symbol for a determinant can be the phrase

det in front of a matrix variable, det(A) or

vertical bars arounda matrix, A or .

Matrix Determinants

To find the determinant of a 2 x 2 matrix,

multiply diagonal 1 and subtract the product of

diagonal 2.

Matrix Determinants

To find the determinant of a 3 x 3 matrix, first

recopy the first two columns. Then do 6 diagonal

products.

Matrix Determinants

The determinant of the matrix is the sum of the

downwards products minus the sum of the upwards

products.

(-8) - (94) -102

Identity Matrices

- An identity matrix is a square matrix that has

1s along the main diagonal and 0s everywhere

else.

- When you multiply a matrix by the identity

matrix, you get the original matrix.

Inverse Matrices

- When you multiply a matrix and its inverse, you

get the identity matrix.

Inverse Matrices

- Not all matrices have an inverse!
- To find the inverse of a 2 x 2 matrix, first find

the determinant. - If the determinant 0, the inverse does not

exist! - The inverse of a 2 x 2 matrix is the reciprocal

of the determinant times the matrix with the main

diagonal swapped and the other terms multiplied

by -1.

Inverse Matrices

- Example 1

Inverse Matrices

- Example 2

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

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

Copyright 2017 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

Copyright 2017 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

The PowerPoint PPT presentation: "MATRICES" 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!