{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lecture Notes (19) - MA 3280 Lecture 19 Determinants Monday...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
MA 3280 Lecture 19 - Determinants Monday, March 24, 2014. Objectives: Material from 8.2 and 8.3: Order 1, 2, and 3 determinants. At the beginning of the semester, and when we talked about Fnding inverse matrices, we used something that is called a determinant . ±or example, given a 2 × 2 matrix (1) A = b a 11 a 12 a 21 a 22 B , we saw that (2) A - 1 = 1 a 11 a 22 - a 12 a 21 b a 22 - a 12 - a 21 a 11 B That funny thing on the bottom is the determinant of A . We’ll use vertical line brackets to denote the determinant, like | A | . A 2 × 2 determinant, therefore, is deFned to be (3) v v v v a 11 a 12 a 21 a 22 v v v v = a 11 a 22 - a 12 a 21 . As an example, (4) v v v v 3 4 7 2 v v v v = (3)(2) - (4)(7) = 6 - 28 = - 22 . Cramer’s Rule. The little trick I showed you to solve a 2 × 2 system of equations can be reformulated in terms of determinants. It turns out that the solution for a system like (5) 2 x 1 + 3 x 2 = 1 5 x 1 + 4 x 2 = 6 has solutions as follows. (6) x 1 = v v v v 1 3 6 4 v v v v v v v v 2 3 5 4 v v v v = 4 - 18 8 - 15 = - 14 - 7 = 2 , and (7) x 2 = v v v v 2 1 5 6 v v v v v v v v 2 3 5 4 v v v v = 12 - 5 8 - 15 = 7 - 7 = - 1 . Do you see the pattern? The determinant on the bottom has the coe²cients on the left side of the equations,
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
Image of page 2
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