Thursday, June 5, 2014

The Matrix, Inverse

For matrices there is no such thing as division, you can multiply but can’t divide.  Multiplying by the inverse matrix results in the same thing.    The inverse of a matrix A is A-1 only when:  A × A-1=  A-1 × A = I.   In other words multiplying a matrix by its inverse equals the identity matrix.

Finding the inverse of a 2x2 matrix is simple; there is a formula for that.  The bigger the matrix the bigger the problem.   There are two methods to find the inverse of a matrix: using minors or using elementary row operations (also called the Gauss-Jordan method), both methods are equally tedious.   We’ll be using the latter to find the inverse of matrices of order 3x3 or larger.   For a review of matrix elementary row operations click here.


This is one of the things you really want Symbolab to do the magic.

Here’s an example of a 2x2 matrix - click here:


I neglected to mention that the formula is using the determinant, Symbolab does that too:
(Click here for the link to the matrix determinant calculator)



Here’s a more advanced example with a 3x3 matrix - click here:


Let’s zoom into the row operations:


…told you it’s no fun

Here’s the link to an example with a 4x4 matrix, not for the weakhearted - click here.


Cheers,
Michal

19 comments:

  1. I have been dotty by reading your blog because it has a unique data.
    epistane

    ReplyDelete
  2. Check out some dissertation acknowledgements examples right now, so it will be easier for you to accomplish such task in the future!

    ReplyDelete
  3. Your blog is very great to tangle with, I can simply say I'm addicted to reading your blog daily. Keep building lives and flying high. credited money

    ReplyDelete
  4. You are very good at that.
    คาสิโนออนไลน์ที่น่าเชื่อถือและมีความเป็นมืออาชีพที่สุดในตอนนี้
    โปรโมชั่นGclub ของทางทีมงานตอนนี้แจกฟรีโบนัส 50%
    เพียงแค่คุณสมัคร สล็อตออนไลน์ กับทางทีมงานของเราเพียงเท่านั้น
    ร่วมมาเป็นส่วนหนึ่งกับเว็บไซต์คาสิโนออนไลน์ของเราได้เลยค่ะ
    สมัครสล็อตออนไลน์ >>> Goldenslot
    สนใจร่วมสนุกกับ คาสิโนออนไลน์ คลิ๊กได้เลย
    มีทั้งคาสิโนออนไลน์ หวยออนไลน์ ฟุตบอลออนไลน์ สล็อตออนไลน์ และอื่นๆอีกมากมาย

    ReplyDelete
  5. We are the best writing company providing Best Assignment Writing Service at affordable rates. Our Research Paper for Sale Online are student-oriented, and therefore we price our articles at student-pocket -friendly rates.

    ReplyDelete
  6. fast social follower will provide you the best social media services such as Buy linkedin connections , Best Place To Buy Linkedin Connections .

    ReplyDelete
  7. Math is queen of knowledge.Thanks for sharing, Visit my site,Dissertation VS Thesis

    ReplyDelete
  8. Agen slot resmi online Indobetsport, menyediakan permainan mesin slot Joker123 dengan menggunakan pulsa. Akun bisa anda dapatkan secara gratis melalui situs-situs resmi Indobetsport.
    login joker123
    link aternatif joker123
    joker123 slot
    joker123 apk
    judi slot joker123
    daftar id joker123
    agen joker123
    joker123 apk
    download joker123
    download joker888
    joker88
    download joker88

    ReplyDelete
  9. It's really a nice and helpful piece of information. I am happy that you shared this useful info with us. Please stay us informed like this. Thank you for sharing.
    John Clarke
    Digi Me
    mcafee.com/activate

    ReplyDelete
  10. ​Hello guys, I am astudent of a Law University in new York and I do not have a lot of spare time due to the pecific of my future profession.
    Previously I was in the search of someone, who would be ready to help me with writing my academic essays and other term papers, in my university is quite important to score a good grade, so the paper should be quite unique and informative
    Finally, I found the froum where one moy recommend me to ask for help of the qualified writers from land paper​ service, and for now I still their client, you will discover here how to do a college book report

    ReplyDelete
  11. It was a great experience being here, love your writing. Bitcoin (BTC) from the beginning to the end.

    ReplyDelete