{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

inverse - Lecture Note 3-1 Dr Jeff Chak-Fu WONG Department...

Info icon This preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
Lecture Note 3-1 Dr. Jeff Chak-Fu WONG Department of Mathematics Chinese University of Hong Kong [email protected] MAT 2310 Linear Algebra and Its Applications Fall, 2007 Produced by Jeff Chak-Fu WONG 1
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
S OLUTIONS OF L INEAR S YSTEMS OF E QUATIONS S OLUTIONS OF L INEAR S YSTEMS OF E QUATIONS 2
Image of page 2
A M ETHOD FOR F INDING THE INVERSE A M ETHOD FOR F INDING THE INVERSE 3
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Let A be an n × n matrix. If A is invertible, then there is a matrix B with AB = 1 0 0 0 0 1 0 0 0 0 . . . 0 0 0 0 1 Let the columns of B be the vectors x 1 , x 2 , · · · , x n . So B = h x 1 x 2 · · · x n i and AB = h A x 1 A x 2 · · · A x n i . A M ETHOD FOR F INDING THE INVERSE 4
Image of page 4
We want AB = I n , so we wish to find the vectors x 1 , x 2 , · · · , x n such that A x 1 = 1 0 0 . . . 0 , A x 2 = 0 1 0 . . . 0 , · · · , A x n =
Image of page 5

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern