// Numbas version: exam_results_page_options {"name": "Matbis 2 - Bab 2 dan 3 - No 5", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Matbis 2 - Bab 2 dan 3 - No 5", "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "

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

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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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