This preview shows pages 1–6. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Lecture Note: Review I: Oct 10  Oct 13, 2006 Dr. Jeff ChakFu WONG Department of Mathematics Chinese University of Hong Kong [email protected] MAT 2310 Linear Algebra and Its Applications Fall, 2006 Produced by Jeff ChakFu WONG 1 L INEAR E QUATIONS AND M ATRICES LINEAR EQUATIONS AND MATRICES 2 1. Method of elimination. To solve a linear system, repeatedly perform the following operations: (a) Interchange two equations . (b) Multiply an equation by a nonzero constant . (c) Add a multiple of one equation to another equation . 2. Matrix Operations. (a) Addition (b) Scalar Multiplication (c) Transpose (d) Multiplication 3. Theorem 0.1 : Properties of matrix addition. 4. Theorem 0.2 : Properties of matrix multiplication. 5. Theorem 0.3 : Properties of scalar multiplication. 6. Theorem 0.4 : Properties of transpose. 7. Reduced row echelon form. 8. Procedure for transforming a matrix to reduced row echelon form. LINEAR EQUATIONS AND MATRICES 3 9. GaussJordan reduction procedure (for solving the linear system A x = b ). 10. Gauss elimination procedure (for solving the linear system A x = b ). 11. Theorem 0.8 : A homogeneous system of m equations in n unknowns always has a nontrivial solution if m < n . 12. Theorem 0.10 : Properties of the inverse. 13. Practical method for finding A 1 14. Theorem 0.12 : An n × n matrix is nonsingular if and only if it is row equivalent to I n . 15. Theorem 0.13 : If an n × n matrix, the homogeneous system A x = has a nontrivial solution if and only if A is singular. LINEAR EQUATIONS AND MATRICES 4 16. List of Nonsingular Equivalences : The following statements are equivalent. (a) A is nonsingular. (b) x = is the only solution to A x = . (c) A is row equivalent to I n ....
View
Full
Document
This note was uploaded on 10/15/2009 for the course MATHEMATIC MAT2310B taught by Professor Jeffwong during the Spring '09 term at CUHK.
 Spring '09
 JeffWong
 Linear Algebra, Algebra

Click to edit the document details