MAT211_Lecture17[1]

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

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

View Full Document Right Arrow Icon
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
Background image of page 1

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

View Full DocumentRight Arrow Icon
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.
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 4

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

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online