MAT211_Lecture17[1]

# MAT211_Lecture17[1] - Recall that a 2 x 2 matrix A a b d...

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

MAT211 Lecture 17 Determinants. Recall that a 2 x 2 matrix A is invertible If and only if a.d-b.c ! 0. The number a.d-b.c is the the determinant of A. a b c d Definition A pattern in an n x n matrix A is a choice of entries of A, such that there is only one entry in each row and only one in each column. Example Find all possible patterns in 2x2 matrices Find all possible patterns in 3x3 matrices. How many patterns are there in 4x4 matrices? And in n x n matrices? Definition The entries of a pattern P of a matrix A are inverted if one of them is located right and above the other in A. The signature of a pattern P of a matrix A, denoted by sgn(P) is (-1) (number of pairs of inverted entries in P) EXAMPLE Find the signature of the pattern of a 3 x 3 matrix A, a 31 , a 22 , a 13

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

View Full Document
Definition The determinant a square matrix A, denoted by det A is " sgn(P).product(elements in P) where the sum is taken over all patterns P.
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