TIM4_Rizka Putri

DETERMINAN FUNGSI
Dosen Pengampu :
Ngatini, S.Si., M.Si.
Nama Kelompok :
1. Bayu Inthan Putri P. (3012010006)
2. Pradipta Shofianisa (3012010027)
3. Rizka Putri (3012010028)
UNIVERSITAS INTERNASIONAL SEMEN INDONESIA
GRESIK
2021

Dapatkan determinan dari matriks berikut dengan metode kofaktor.
Sederhanakan dengan di lakukan OBE
1 2 3 4
8 7 6 5
[
]
9 −1 −2 −3
−4 −5 −5 −4
Penyelesaian 1 :
1. Metode OBE
1 2 3 4
0 −3 −4 −3
[
]B2 = B2 + (2)B4
9 −1 −2 −3
−4 −5 −5 −4
1 2 3 4
0 −3 −4 −3
[
]B3 = B3 + (-9)B1
0 −19 −29 −39
−4 −5 −5 −4
1 2 3 4
0 −3 −4 −3
[
]B4 = B4 + (4)B1
0 −19 −29 −39
0 3 7 12
8 7 6 5
-8 -10 -10 -8
0 -3 -4 -3
9 -1 -2 -3
-9 -18 -27 -36
0 -19 -29 -39 +
-4 -5 -5 -4
4 8 12 16
0 3 7 12
+
+
2. Metode Kofaktor
+ 1 2 3 4
−3 − 4 − 3
0 −3 −4 −3
- [
] = (1) · [ −19
0 −19 −29 −39
− 29 −39]
+
3 7 12
0 3 7 12
-

Nomor 1, 2, dan 3 dengan Ekspansi Kolom Pertama
+ −3 −4 − 3
1. - [ −19 −29 −39]
3 7 12
+
+ −3 −4 − 3
2. - [ −19 −29 −39]
3 7 12
+
+ −3 −4 − 3
3. - [ −19 −29 −39]
3
+
7 12
−29 −39
= (1) (-3) |
7 12 |
= (-3) ((-29 ·12 – (-39) · 7)
= (-3) (-348 – (-273))
= (-3) (-75)
= 225
−4 −3
= (1) (19) |
7 12 |
= (19) ((-4) · 12 – (-3) · 7)
= (19) (-48 – (-21))
= (19) (-27)
= -513
−4 −3
= (1) (3) |
−29 −39 |
= (3) ((-4) · (-39) – (-3) · (-29)
= (3) (156 – 87)
= (3) (69)
= 207
1 2 3 4
8 7 6 5
det[
] = 225 – 513 + 207 = -81
9 −1 −2 −3
−4 −5 −5 −4

Penyelesaian 2 :
1 2 3 4
8 7 6 5
[
]
9 −1 −2 −3
−4 −5 −5 −4
1 2 3 4
8 7 6 5
1. [
]B3 = B3 – B2
1 −8 −8 −8
−4 −5 −5 −4
1 2 3 4
0 −3 −4 −3
2. [
]B2 = B2 +(2)B4
1 −8 −8 −8
−4 −5 −5 −4
1 2 3 4
0 −3 −4 −3
3. [
]B3 = B3 – B1
0 −10 −11 −12
−4 −5 −5 −4
4. [
1 2 3 4
0 −3 −4 −3
]B4 = B4 + (4)B1
0 −10 −11 −12
0 3 7 12
+
-
+
-
[
1 2 3 4
−3 − 4 − 3
0 −3 −4 −3
] = (1) · [ −10
0 −10 −11 −12
− 11 −12]
3 7 12
0 3 7 12

−3 −4 − 3
1. (1) · [ 0 37 84] B2 = (3)B2 + (10)B3
3 7 12
−3 −4 − 3
2. (1) · [ 0 37 84] B3 = B3 + B1
0 3 9
−1 − 4 − 1
3
3. (1) · [ 0 37 84
] B1 = (1/3)B1
0 3 9
−1 − 4 − 1
3
(1) · [ 0 37 84
]
0 3 9
+
-
+
37 84
(1) [
3 9 ]
= (1)(-1)(37·9 – 84·3)
= - (333 – 252)
= - 81