Linear_Algebra_03 - Solving Systems of Linear Equations by...

Info icon This preview shows pages 1–4. Sign up to view the full content.

Solving Systems of Linear Equations by the Gaussian Elimination and Gauss-Jordan Elimination Methods J. Vanualailai * April 26, 2013 * School of Computing, Information & Mathematical Sciences, University of the South Pacific, Suva, Fiji.
Image of page 1

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

Systems of Linear Equations In general, a system of linear equations has m equations and n variables denoted by x 1 ,x 2 , · · · ,x n . a 11 x 1 + a 12 x 2 + a 13 x 3 + · · · + a 1 n x n = b 1 a 21 x 1 + a 22 x 2 + a 23 x 3 + · · · + a 2 n x n = b 2 a 31 x 1 + a 23 x 2 + a 33 x 3 + · · · + a 3 n x n = b 3 . . . . . . . . . . . . . . . . . . a m 1 x 1 + a m 2 x 2 + a m 3 x 3 + · · · + a mn x n = b m In matrix form, this is A x = b where A = a 11 a 12 a 13 · · · a 1 n a 21 a 22 a 23 · · · a 2 n a 31 a 23 a 33 · · · a 3 n . . . . . . . . . . . . . . . a m 1 a m 2 a m 3 · · · a mn , x = x 1 x 2 x 3 . . . x n , b = b 1 b 2 b 3 . . . b m
Image of page 2
Augmented Matrix We will study two methods that uses matrices to solve our system of
Image of page 3

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

Image of page 4
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