Difference between r1.6 and the current
@@ -1,3 +1,6 @@
선형대수 이상화 보는중.
[[https://www.youtube.com/watch?v=i3VTeQW0Tw4&list=PLSN_PltQeOyjDGSghAf92VhdMBeaLZWR3&index=2]]
Sub:
@@ -8,3 +11,32 @@
[[기저,basis]]
Twin: [[VG:선형대수,linear_algebra]]
Twin: [[VG:선형대수,linear_algebra]]
= GE =
[[가우스소거법Gaussian_elimination]]
[[VG:가우스_소거,Gaussian_elimination]]
{
ex 1
$\begin{cases}2u&+v&+w&=&5\\4u&-6v&&=&-2\\-2u&+7v&+2w&=&9\end{cases}$
첫째줄은 그대로 두고,
두째줄은 ②-①×2,
셋째줄은 ③+①
$\begin{cases}2u&+v&+w&=&5\\&-8v&-2w&=&-12\\&8v&+3w&=&14\end{cases}$
③+② 하면
$\begin{cases}2u&+v&+w&=&5\\&-8v&-2w&=&-12\\&&w&=&2\end{cases}$
한편 계수들을 가지고 행렬을 만들면
$\left[\begin{array}{rrr.r}2&1&1&5\\4&-6&0&-2\\-2&7&2&9\end{array}\right]$
$\left[\begin{array}{rrr.r}2&1&1&5\\0&-8&-2&-12\\0&8&3&14\end{array}\right]$
$\left[\begin{array}{rrr.r}2&1&1&5\\0&-8&-2&-12\\0&0&1&2\end{array}\right]$
이 행렬을 upper triangular matrix라고 한다.
ex 2
## 3x3행렬: $\left[\begin{array}{rrr.r}&&&\\&&&\\&&&\end{array}\right]$
$\left[\begin{array}{rrr.r}1&1&1&a\\2&2&5&b\\4&4&8&c\end{array}\right]$
$\left[\begin{array}{rrr.r}1&1&1&a\\0&0&3&b-2a\\0&0&4&c-4a\end{array}\right]$
}
= LU factorization/decomposition =
선형대수 이상화 보는중.
![[https]](/wiki/imgs/https.png)
https://www.youtube.com/watch?v=i3VTeQW0Tw4&list=PLSN_PltQeOyjDGSghAf92VhdMBeaLZWR3&index=2
https://www.youtube.com/watch?v=i3VTeQW0Tw4&list=PLSN_PltQeOyjDGSghAf92VhdMBeaLZWR3&index=2Up: 수학,math
GE ¶
ex 1
$\displaystyle \begin{cases}2u&+v&+w&=&5\\4u&-6v&&=&-2\\-2u&+7v&+2w&=&9\end{cases}$
첫째줄은 그대로 두고,
두째줄은 ②-①×2,
셋째줄은 ③+①
$\displaystyle \begin{cases}2u&+v&+w&=&5\\&-8v&-2w&=&-12\\&8v&+3w&=&14\end{cases}$
③+② 하면
$\displaystyle \begin{cases}2u&+v&+w&=&5\\&-8v&-2w&=&-12\\&&w&=&2\end{cases}$
첫째줄은 그대로 두고,
두째줄은 ②-①×2,
셋째줄은 ③+①
$\displaystyle \begin{cases}2u&+v&+w&=&5\\&-8v&-2w&=&-12\\&8v&+3w&=&14\end{cases}$
③+② 하면
$\displaystyle \begin{cases}2u&+v&+w&=&5\\&-8v&-2w&=&-12\\&&w&=&2\end{cases}$
한편 계수들을 가지고 행렬을 만들면
$\displaystyle \left[\begin{array}{rrr.r}2&1&1&5\\4&-6&0&-2\\-2&7&2&9\end{array}\right]$
$\displaystyle \left[\begin{array}{rrr.r}2&1&1&5\\0&-8&-2&-12\\0&8&3&14\end{array}\right]$
$\displaystyle \left[\begin{array}{rrr.r}2&1&1&5\\0&-8&-2&-12\\0&0&1&2\end{array}\right]$
이 행렬을 upper triangular matrix라고 한다.
$\displaystyle \left[\begin{array}{rrr.r}2&1&1&5\\4&-6&0&-2\\-2&7&2&9\end{array}\right]$
$\displaystyle \left[\begin{array}{rrr.r}2&1&1&5\\0&-8&-2&-12\\0&8&3&14\end{array}\right]$
$\displaystyle \left[\begin{array}{rrr.r}2&1&1&5\\0&-8&-2&-12\\0&0&1&2\end{array}\right]$
이 행렬을 upper triangular matrix라고 한다.
ex 2
$\displaystyle \left[\begin{array}{rrr.r}1&1&1&a\\2&2&5&b\\4&4&8&c\end{array}\right]$
$\displaystyle \left[\begin{array}{rrr.r}1&1&1&a\\0&0&3&b-2a\\0&0&4&c-4a\end{array}\right]$
}
$\displaystyle \left[\begin{array}{rrr.r}1&1&1&a\\2&2&5&b\\4&4&8&c\end{array}\right]$
$\displaystyle \left[\begin{array}{rrr.r}1&1&1&a\\0&0&3&b-2a\\0&0&4&c-4a\end{array}\right]$
}