Tugas Matematika Terapan Ii_ Trivena Ngantung_ 2b Kbg D4.docx

NAMA : TRIVENA AGATA NGANTUNG NIM : 18012050 KELAS : II B KBG D4 Soal : 1. 3 x + 6 y = 24 2 x – 3 y = -5 Dapat ditulis dalam bentuk matriks : [

24 3 6 𝑥 ]{ } = { } 2 −3 𝑦 −5

𝑝𝑒𝑛𝑦𝑒𝑙𝑒𝑠𝑎𝑖𝑎𝑛: 3 6 |𝐷| = | | = −9 − 12 = −21 2 −3 |𝐷𝑥| = | 24 6 | = −72 + 30 = −42 −5 −3 |𝐷𝑦| = |3 24 | = −15 − 48 = −63 2 −5 Jadi : 𝐷𝑥 −42 𝑥=| |= =2 𝐷 −21 𝐷𝑦 −63 𝑦=| |= =3 𝐷 −21 2. 2 x + 3 y – z = 20 4 x - 2 y – 5 z = 23 x + 3 y + 4 z = 19 Dapat ditulis dalam bentuk matriks : 2 3 −1 𝑥 20 [4 −2 5 ] {𝑦} = {23} 1 3 4 𝑧 19

Penyelesaian : 2 3 −1 |𝐷| = |4 −2 5 | = 2 |−2 5| − 3 |4 5| + (−1) |4 −2| 1 3 3 4 1 4 1 3 4 = 2 ((−8) − 15) − 3(16 − 5) − 1(12 − (−2)) =2 (−23) − 3(11) − 1(14) = (−46) − 33 − 14 = −93 20 |𝐷𝑥| = |23 19

3 −1 −2 5 23 | − 3| −2 5 | = 20 | 3 4 19 3 4

23 5 | + (−1) | 19 4

= 20 ((−8) − 15) − 3(92 − 95) − 1(69 − (−38)) = 20 (−23) − 3(−3) − 1(107) = (−460) + 9 − 107 = −558 = - 460+ 9 - 107= -558 2 20 |𝐷𝑦| = |4 23 1 19

−1 23 5 | = 2| 19 4

5 4 | − 20 | 4 1

4 23 5 | + (−1) | | 1 19 4

= 2 (92 − 95) − 20(16 − 5) − 1(76 − 23) =2 (−3) − 20 (11) − 1(53) = −279 2 3 20 |𝐷𝑧| = |4 −2 23| = 2 |−2 23| − 3 |4 23| + 20 |4 −2| 3 19 1 19 1 3 1 3 19 = 2 ((−38) − 69) − 3 (76 − 23) + 20 (12 (−2)) =2 -38-69-3 76-23+20 (12 -2) =2 (−107) − 3 (53) + 20 (14) = −93 Jadi : 𝐷𝑥 −558 𝑥=| |= =6 𝐷 −93 𝐷𝑦 −279 𝑦=| |= =3 𝐷 −93 𝑧=|

𝐷𝑧 −93 |= =1 𝐷 −93

−2 | 3