# 미지수가 n개인 연립일차방정식의 근(해)과 계수(Rank)와의 관계
![](https://velog.velcdn.com/images/grovy52/post/8b3413ef-481b-4d3c-91e2-0b52493d26d4/image.png)
(2) 오직 하나 존재한다 = 유일한 해를 갖는다
(3) ~이외의 해를 갖는다.
# 예제
1.
![](https://velog.velcdn.com/images/grovy52/post/0531b629-2eee-4c31-b8e7-ce467985395c/image.png)
![](https://velog.velcdn.com/images/grovy52/post/8085783c-4e50-4284-b3fa-af623c8a6c48/image.png)
2.
![](https://velog.velcdn.com/images/grovy52/post/73b9b6c3-4ac8-4a2b-a53a-9455198b7f4f/image.png)
![](https://velog.velcdn.com/images/grovy52/post/9c609d27-ec1a-4927-9da1-bebaf3563838/image.png)
3.
![](https://velog.velcdn.com/images/grovy52/post/70a7f5c4-74b3-4d1c-9f42-6f2ecb5f3d9f/image.png)
4.
![](https://velog.velcdn.com/images/grovy52/post/9e992558-824d-482a-958b-068109f29b5f/image.png)
5.
![](https://velog.velcdn.com/images/grovy52/post/7968f854-57b7-4654-8b33-9dadc0945982/image.png)
6.
![](https://velog.velcdn.com/images/grovy52/post/b6bdb61c-3790-4b77-88e7-cf0a560c57e0/image.png)
7.
![](https://velog.velcdn.com/images/grovy52/post/5d317676-63d4-4df0-8471-96eb56e29a3a/image.png)
8.
![](https://velog.velcdn.com/images/grovy52/post/54c2440a-80a5-4c78-a491-194f4f7ad64e/image.png)
9.
![](https://velog.velcdn.com/images/grovy52/post/c0c4bb27-bd5a-4e84-994c-8be467fc06e5/image.png)
그 밖의 특성
1. 선형방정식의 경우, 계수행렬과 확대 행렬의 랭크가 같다.
Rank(A) = Rank(A|B) = 2
![](https://velog.velcdn.com/images/grovy52/post/7210999b-8e62-4d44-b842-fa43ba224011/image.png)
Rank(A) = Rank(A|B) = 1
![](https://velog.velcdn.com/images/grovy52/post/8486f636-d675-40e6-aaf2-b9717b81a8da/image.png)
2. A가 n x n 행렬일때,
( |A| = deterimmnant A = A의 행렬식 )
(1) |A|가 0이 아님. = Rank(A) = n
(2) |A|가 0임. = Rank(A) < n