st","extracted_subject":"MATH","extracted_chapter":"DETERMINANTS AND MATRICES","extracted_topic":"EXPANSION OF DETERMINANTS, SOLUTION OF EQUATION","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_2165.png?top_left_x=532&top_left_y=1510&width=532&height=327&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e74425d76b7ab320ba5","slug":"one-root-of-the-equation-left-beginmatrix-3x8-3-3-","content":"One root of the equation \\(\\left| \\begin{matrix}\n3x–8 & 3 & 3 \\\\\n3 & 3x–8 & 3 \\\\\n3 & 3 & 3x–8\n\\end{matrix} \\right|\\) = 0 is –","options":[{"_id":"68a95c527f15af4716d55586","text":"8/3","sequence":0,"isCorrect":false},{"_id":"68a95c527f15af4716d55587","text":"2/3","sequence":1,"isCorrect":true},{"_id":"68a95c527f15af4716d55588","text":"1/3","sequence":2,"isCorrect":false},{"_id":"68a95c527f15af4716d55589","text":"16/3","sequence":3,"isCorrect":false}],"correct_answer":"2/3","explanation":"Let C₁ → C₁ + C₂ + C₃; C₂ → C₂ – C₃\n\n\\(\\left| \\begin{matrix}\n3x–2 & 0 & 3 \\\\\n3x–2 & 3x–11 & 3 \\\\\n3x–2 & 11–3x & 3x–8\n\\end{matrix} \\right|\\) = 0\n\n∴ X = 2/3 is one root.","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:40.086Z","__v":0,"vector_store_id":"2b200ec6-5f85-46bb-a756-792c26f9b68a","updated_at":"2024-08-30T21:49:40.086Z","isStarred":false},"params":{"questionSlug":"one-root-of-the-equation-left-beginmatrix-3x8-3-3-"}}]}]]

Question: One root of the equation \(\left| \begin{matrix} 3x–8 & 3 & 3 \\ 3 & 3x–8 & 3 \\ 3 & 3 & 3x–8 \end{m...

Solution