ROOT
BISECTION
FALSE-POSITION
FIXED-POINT
NEWTON-RAPHSON
SECANT
LINEAR EQUATION
CRAMER'S RULE
GAUSS ELIMINATION
GAUSS-JORDAN ELIMINATION
MATRIX INVERSION
LU DECOMPOSITION
CHOLESKY DECOMPOSITION
JACOBI ITERATION
GAUSS-SEIDEL ITERATION
INTERPOLATION
NEWTON DIVIDED-DIFFERENCES
LAGRANGE INTERPOLATION
SPLINE INTERPOLATION
EXTRAPOLATION
SIMPLE REGRESSION
MULTIPLE REGRESSION
/gauss_jordan_elimination
Definition
A
=
[
a
11
a
12
a
13
a
21
a
22
a
23
a
31
a
32
a
33
]
→
G
a
u
s
s
−
J
o
r
d
a
n
e
l
i
m
i
n
a
t
i
o
n
A
=
[
1
0
0
0
1
0
0
0
1
]
A = \begin{bmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{bmatrix} \xrightarrow{Gauss-Jordan\:elimination} A = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}
A
=
a
11
a
21
a
31
a
12
a
22
a
32
a
13
a
23
a
33
G
a
u
ss
−
J
or
d
an
e
l
imina
t
i
o
n
A
=
1
0
0
0
1
0
0
0
1
Matrix
Matrix size (NxN)
Reset
[
A
]
[A]
[
A
]
a
11
a_{11}
a
11
a
12
a_{12}
a
12
a
13
a_{13}
a
13
a
14
a_{14}
a
14
a
21
a_{21}
a
21
a
22
a_{22}
a
22
a
23
a_{23}
a
23
a
24
a_{24}
a
24
a
31
a_{31}
a
31
a
32
a_{32}
a
32
a
33
a_{33}
a
33
a
34
a_{34}
a
34
a
41
a_{41}
a
41
a
42
a_{42}
a
42
a
43
a_{43}
a
43
a
44
a_{44}
a
44
{
x
}
\{x\}
{
x
}
x
1
x_1
x
1
x
2
x_2
x
2
x
3
x_3
x
3
x
4
x_4
x
4
[
B
]
[B]
[
B
]
=
=
=
[
B
]
[B]
[
B
]
b
1
b_1
b
1
b
2
b_2
b
2
b
3
b_3
b
3
b
4
b_4
b
4
Calculate