{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

section17 - Chapter 1 MAT188H1F Lec03 Burbulla Chapter 1...

This preview shows pages 1–3. Sign up to view the full content.

Chapter 1 MAT188H1F Lec03 Burbulla Chapter 1 Lecture Notes Fall 2007 Chapter 1 Lecture Notes MAT188H1F Lec03 Burbulla Chapter 1 Chapter 1 1.7: LU -Factorization Chapter 1 Lecture Notes MAT188H1F Lec03 Burbulla

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

View Full Document
Chapter 1 1.7: LU -Factorization Example 4 From Section 1.2, Again Consider the system of equations in three variables x 1 , x 2 and x 3 : 2 x 1 + x 2 - x 3 = 1 x 1 + x 2 + x 3 = 6 - 3 x 1 + 2 x 2 + 4 x 3 = 13 This can be written as a single matrix equation AX = B , with A = 2 1 - 1 1 1 1 - 3 2 4 , X = x 1 x 2 x 3 , B = 1 6 13 . Now consider the matrices L = 1 0 0 1 / 2 1 0 - 3 / 2 7 1 and U = 2 1 - 1 0 1 / 2 3 / 2 0 0 - 8 . Chapter 1 Lecture Notes MAT188H1F Lec03 Burbulla Chapter 1 1.7: LU -Factorization A = LU L is a lower triangular matrix and U is an upper triangular matrix. You can check that A = LU . This is called an LU factorization of A . It can be used to solve the system AX = B in a different, more computer friendly way, in two steps: ( LU ) X = B LY = B and UX = Y .
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

• 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.

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

• 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.

Dana University of Pennsylvania ‘17, Course Hero Intern

• 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.

Jill Tulane University ‘16, Course Hero Intern