// Numbas version: exam_results_page_options {"name": "Set Soal Matematika Bisnis II - Bab 2 dan 3", "metadata": {"description": "", "licence": "None specified"}, "duration": 2700, "percentPass": 0, "showQuestionGroupNames": false, "showstudentname": true, "question_groups": [{"name": "PG + Isian", "pickingStrategy": "all-shuffled", "pickQuestions": 1, "questionNames": ["", "", "", ""], "questions": [{"name": "Matbis 2 - Bab 2 dan 3 - No 1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Meong Meong Project", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4687/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "

Pilihlah seluruh nilai $a$, $b$, dan $c$ agar sistem persamaan linier $\\begin{cases} \\var{a}x-\\var{b}y &= c \\\\ ax-by &= \\var{c} \\end{cases}$ mempunyai banyak solusi.

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Pilihlah seluruh sistem persamaan linier yang bersifat underdetermined.

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Jumlah nilai $k$ yang memenuhi persamaan $\\begin{bmatrix} 2 & 2 & k \\end{bmatrix}\\begin{bmatrix} 1 & 2 & 0 \\\\ 2 & 0 & 3 \\\\ 0 & 3 & 1 \\end{bmatrix}\\begin{bmatrix} 2 \\\\ 2 \\\\ k \\end{bmatrix} = \\simplify{-k^2+{a}k+{b}}$ adalah $\\ldots$.

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Sebuah ekonomi terdiri dari dua buah industri: perikanan dan peternakan. Untuk memproduksi $1$ unit produk perikanan diperlukan $0.4$ unit produk perikanan sendiri dan $0.3$ unit produk peternakan. Sedangkan untuk memproduksi $1$ unit produk peternakan diperlukan $0.4$ unit produk perikanan dan $0.3$ unit produk peternakan sendiri. Permintaan konsumen akan produk perikanan dan peternakan berturut-turut adalah senilai $210$ ribu dolar dan $300$ ribu dolar.

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Tentukan jumlah produk peternakan yang diperlukan (dalam ribu dolar) dalam proses internal untuk memenuhi output kotor (gross output).

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Diberikan matriks $M=\\begin{bmatrix} \\var{a} & \\var{b} \\\\ \\var{b} & \\var{a} \\end{bmatrix}$.

Misal $\\lambda_1$ dan $\\lambda_2$ adalah nilai eigen dari matriks $M$ dengan $\\lambda_1< \\lambda_2$. Maka $\\lambda_1$ dan $\\lambda_2$ berturut-turut adalah $\\ldots$.

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Diketahui $\\mathbf{v}_1 = \\begin{bmatrix} -1 \\\\ a \\end{bmatrix}$ dan $\\mathbf{v}_2 = \\begin{bmatrix} b \\\\ 1 \\end{bmatrix}$ berturut-turut adalah vektor eigen yang berkaitan dengan $\\lambda_1$ dan $\\lambda_2$. Misal $\\mathbf{v} = \\begin{bmatrix} 0 \\\\ 1 \\end{bmatrix}$. Tentukan $M^{5}\\mathbf{v}$.

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Berdasarkan matriks $M$ yang diberikan, pilihlah seluruh pernyataan yang tepat.

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Waktunya 5 menit lagi ya.

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Selamat datang!

Silakan gunakan set soal ini dengan bijak. Kalian bisa mencoba set soal ini terus-menerus.

Set soal ini dapat digunakan oleh siapapun secara gratis.

Petunjuk pengerjaan soal:

Jawaban dapat dituliskan dalam bentuk desimal maupun pecahan.
Jika jawaban dituliskan dalam bentuk desimal, pisahkan dengan tanda titik dan bulatkan hingga dua angka di belakang titik. Contoh: ketik 0.67 untuk menjawab \$\\frac{2}{3}\$.
Jika jawaban dituliskan dalam bentuk pecahan, pisahkan pembilang dan penyebut dengan garis miring dan jawab dengan pecahan paling sederhana. Contoh: ketik 2/3 untuk menjawab \$\\frac{2}{3}\$.

Jika ada kunci jawaban yang salah, kalian dapat memberitahu kami di Instagram @meongmeongproject atau OA Line @eog7710d.

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