test","extracted_subject":"MATH","extracted_chapter":"DETERMINANTS AND MATRICES","extracted_topic":"MINOR AND CO-FACTORS, PRODUCT OF DETERMINANTS","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_2181.png?top_left_x=1064&top_left_y=0&width=532&height=327&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e74425d76b7ab320d44","slug":"if-left-beginmatrix-an-an-1-an-2-bn-bn-1-bn-2-cn-c","content":"If \\(\\left| \\begin{matrix}\na^{n} & a^{n + 1} & a^{n + 2} \\\\\nb^{n} & b^{n + 1} & b^{n + 2} \\\\\nc^{n} & c^{n + 1} & c^{n + 2}\n\\end{matrix} \\right|\\) = (a – b) (b – c) (c – a), then n is equal to","options":[{"_id":"68a391a57f15af4716b9b3dc","text":"n =1","sequence":0,"isCorrect":false},{"_id":"68a391a57f15af4716b9b3dd","text":"n = 2","sequence":1,"isCorrect":false},{"_id":"68a391a57f15af4716b9b3de","text":"Any value of n","sequence":2,"isCorrect":false},{"_id":"68a391a57f15af4716b9b3df","text":"None of these","sequence":3,"isCorrect":true}],"correct_answer":"None of these","explanation":"aⁿbⁿcⁿ \\(\\left| \\begin{matrix}\n1 & a & a^{2} \\\\\n1 & b & b^{2} \\\\\n1 & c & c^{2}\n\\end{matrix} \\right|\\)\n\naⁿbⁿcⁿ (a – b) (b – c) (c – a)\n\nŽ comparing with R.H.S\n\nn = 0","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:40.244Z","__v":0,"vector_store_id":"accda91e-a4ed-42a1-bca2-0271507fc71d","updated_at":"2024-08-30T21:49:40.244Z","isStarred":false},"params":{"questionSlug":"if-left-beginmatrix-an-an-1-an-2-bn-bn-1-bn-2-cn-c"}}]}]]

Question: If \(\left| \begin{matrix} a^{n} & a^{n + 1} & a^{n + 2} \\ b^{n} & b^{n + 1} & b^{n + 2} \\ c^{n} &...

Solution