LKPD Matriks [PDF]

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DETERMINAN MATRIKS



Nama Anggota Kelompok 1. _________________ 2. _________________ 3. _________________ 4. _________________



Disusun Oleh: Fitro Arrohmah



Nama Sekolah



: SMK BISA



Mata Pelajaran



: Matematika



Komp. Keahlian : Semua Keahlian Kelas/Semester



: XI / Ganjil



Tahun Pelajaran : 2018-2019 Alokasi Waktu



:



1 JP (45 menit)



A. Kompetensi Dasar 3.16 Menetukan nilai determinan, invers dan tranpos pada ordo 2 x 2 dan nilai determinan dan tranpos pada ordo 3 x 3 4.16 Menyelesaikan masalah yang berkaitan dengan determinan, invers dan tranpose pada ordo 2 x 2 serta nilai determinan dan tranpos pada ordo 3x3 B. Indikator Pencapaian Kompetensi 3.16.1 Menentukan nilai determinan 2x2 3.16.2 Menentukan nilai determinan 3 x 3 4.16.1 Menyelesaikan permasalahan nyata dengan menggunakan determinan dan invers matriks ordo 2x2 dan ordo 3 x 3 C. Tujuan Pembelajaran Melalui diskusi dan menggali informasi untuk menumbuhkan sikap kreatif demokratis peserta didik dapat : -



menentukan nilai determinan matriks ordo 2x2 dengan aturan sarrus menentukan nilai determinan matriks ordo 3x3 dengan aturan sarrus dan ekspansi kofaktor menyelesaikan permasalahan nyata dengan menggunakan determinan



ordo 2x2 dan ordo 3x3



Petunjuk: 1. Tulislah nama anggota kelompok pada LKPD yang sudah disediakan. 2. Berdiskusilah dengan kelompok kalian dengan saling memberi masukan dan saran dalam menyelesaikan soalsoal berikut. 3. Bertanyalah kepada guru jika kalian mengalami kesulitan 4. Kerjakan dengan sungguh-sungguh dengan penuh tanggung jawab.



Lembar Kerja Peserta Didik A. Memahami determinan matriks ordo 2 ×2 Khusus untuk matriks ordo 2 ×2, nilai determinannya merupakan hasil kali elemen–elemen pada diagonal utama dikurangi hasil kali elemen–elemen pada diagonal samping



[ ac bd ] maka determian matriks A adalah :



A=



det A=| A|= a b =ad −bc c d



[ ]



Contoh:



[ 42 13 ] maka hasil kali antara 4 dan



Jika diketahui matriks A=



3 dikurangi hasil kali 2 dan 1, yaitu 12 – 2 = 10 dinamakan determinan. Determinan sebuah matriks adalah sebuah angka atau skalar yang diperoleh dari elemen–elemen matriks tersebut dengan operasi tertentu. B. Memahami determinan matriks ordo 3 ×3 Untuk menentukan determinan matriks ordo 3 ×3 , yaitu dengan meletakkan lagi elemen–elemen kolom pertama dan kedua di sebelah kanan kolom ketiga. a b c A= d e f maka determian matriks A adalah : Jika g h i



[ ]



Setelah memahami materi di atas diskusikan dengan masing-masing kelompok sesuai petunjuk! 1. Diketahui A =



[ 41 −22 ], B = [ 31 32], tentukan determinan dari A + B!



Jawab: ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ............................................................................................................................ ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... 2. Jika det A Diketahui A =



[ 2a 14 ] = 5. Tentukan nilai a!



Jawab: ...................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ............. ..................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... .............. .................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ........ ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... .



3. Buatlah suatu matriks 3 x 3 menurut kalian sendiri kemudian tentukan determinan matriksnya menggunakan ekspansi kofaktor dan kaidah sarrus! Jawab: ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ............................................................................................................................ ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ............................................................................................................................ 4. Pada tahun ajaran baru, anas mewakili temannya untuk membeli 5 buku matematika dan 4 buku biologi. Dia harus membayar sebesar Rp. 410.000,00. Pada saat yang bersamaan, samat mewakili teman-temannya yang lainnya membeli 10 buku matematika dan 6 buku biologi. Samad harus membayar Rp.740.000,00 untuk semuannya. Nyatakan permasalahan tersebut dengan bentuk matriks dan gunakan determinan matriks untuk menyelesaikan persoalan tersebut! Jawab: ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ............................................................................................................................ ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ............................................................................................................................



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