mat 2310 0607_2_note2

mat 2310 0607_2_note2 - Lecture Note 2: Jan 22 - 24, 2007...

Info iconThis preview shows pages 1–12. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Lecture Note 2: Jan 22 - 24, 2007 Dr. Jeff Chak-Fu WONG Department of Mathematics Chinese University of Hong Kong [email protected] MAT 2310C Linear Algebra and Its Applications Spring, 2007 Produced by Jeff Chak-Fu WONG 1 D ETERMINANTS 1. Definition and Properties 2. Cofactor Expansion and Applications DETERMINANTS 2 Our aim is: 1. to know the notion of a determinant, 2. to study some of its properties, and 3. to calculate the determinant of the given matrix via the reduction to triangular form. DETERMINANTS 3 D EFINITION AND P ROPERTIES 1. Permutation 2. Definition of Determinant 3. Properties of Determinants DEFINITION AND PROPERTIES 4 Definition: Let S = { 1 , 2 ,...,n } be the set of integers from 1 to n , arranged in ascending order. A rearrangement j 1 j 2 ...j n of the elements of S is called a permutation of S . DEFINITION AND PROPERTIES 5 D EFINITION OF D ETERMINANT DEFINITION OF DETERMINANT 6 Definition: Let A = [ a ij ] be an n × n matrix. We define the determinant of A (written det( A ) or | A | ) by det( A ) = | A | = X ( ± ) a 1 j 1 a 2 j 2 ...a nj n , (1) where the summation ranges over all permutations j 1 j 2 ...j n of the set S = { 1 , 2 ,...,n } . DEFINITION OF DETERMINANT 7 P ROPERTIES OF D ETERMINANTS PROPERTIES OF DETERMINANTS 8 Theorem 0.1 The determinants of a matrix and its transpose are equal, that is det( A T ) = det( A ) . PROPERTIES OF DETERMINANTS 9 Theorem 0.2 If matrix B results from matrix A by interchanging two rows (columns) of A , then det( B ) =- det( A ) . PROPERTIES OF DETERMINANTS 10 Theorem 0.3 If two rows (columns) of A are equal, then det( A ) = 0 ....
View Full Document

This note was uploaded on 06/05/2011 for the course MATH 3333 taught by Professor Jeffwong during the Spring '11 term at CUHK.

Page1 / 35

mat 2310 0607_2_note2 - Lecture Note 2: Jan 22 - 24, 2007...

This preview shows document pages 1 - 12. Sign up to view the full document.

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