선형시스템의 행렬표현 및 해법elearning.kocw.net/contents4/document/lec/2013/Chungbuk/...• 행 사다리꼴(row echelon form) 로 만든 다음, 맨 아래 부터 변수값을

Matrix Representation of Linear Systems

and their Solution

Keon M. Lee

:

: ,

: Gauss-Jordan , Gauss

(linear system; system of linear equations )

( solution set) (, solution) :

(, ; equivalent)

1. , 2. , 3. .

(augmented matrix)

(Coefficient matrix )

(augmented matrix )

(row operation) (exchange) . (scalar multiplication) 0 . (replace) .

(row operation) (exchange) . (scalar multiplication) 0 . (replace) .

(row operation) (exchange) . (scalar multiplication) 0 . (replace) .

( , row equivalent) , (row equivalent).

(augmented matrix) , (solution set) .

(row reduction)

(row) pivot (leading entry) 0

Image source: http://www.3bktj.co.uk/wood5.htm

(row echelon form) 0 pivot pivot pivot 0

(reduced row echelon form, rref) pivot 1 pivot 0

( )

Image source: http://www.3bktj.co.uk/wood5.htm

(row reduction algorithm) Gauss-Jordan (elimination method) 1. (augmented matrix) 2. (reduced row echelon form)

1. 0 2. 0 pivot 1 3. pivot 0

4. 0 , (inconsistent). Stop

3. rref (solution)

inconsistent (, no solution)

free variable ( ) : z parameter ()

(row reduction algorithm) Gauss

(row echelon form) ,

Summary

.

, , 3 .

(augmented matrix) (, , ) .

(row) pivot 0 .

(row echelon form) pivot 0 .

(reduced row echelon form, rref) pivot 1

.

(row reduction algorithm) , Gauss , Gauss-Jordan .

2 4 (row reduction) 13 14 15 Summary