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_2164.png?top_left_x=0&top_left_y=782&width=532&height=327&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e74425d76b7ab320b8f","slug":"if-fx-left-beginmatrix-a---1-0-ax-a---1-ax2-ax-a-e","content":"If f(x) = \\(\\left| \\begin{matrix}\na & - 1 & 0 \\\\\nax & a & - 1 \\\\\nax^{2} & ax & a\n\\end{matrix} \\right|\\), then f(2x) –f(x) equals","options":[{"_id":"68a370597f15af4716b41b10","text":"a (2a + 3x)","sequence":0,"isCorrect":false},{"_id":"68a370597f15af4716b41b11","text":"ax (2a + 3x)","sequence":1,"isCorrect":true},{"_id":"68a370597f15af4716b41b12","text":"ax (2x + 3a)","sequence":2,"isCorrect":false},{"_id":"68a370597f15af4716b41b13","text":"x (2a + 3x)","sequence":3,"isCorrect":false}],"correct_answer":"ax (2a + 3x)","explanation":"Apply R₂ → R₂ – xR₁, R₃ → R₃ –xR₂ we get\n\nf(x) = \\(\\left| \\begin{matrix}\na & - 1 & 0 \\\\\n0 & a + x & - 1 \\\\\n0 & 0 & a + x\n\\end{matrix} \\right|\\)= a (a + x)²\n\nf(2x) – f(x) = a(a + 2x)² – a (a + x)² = ax (2a + 3x)","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:40.084Z","__v":0,"vector_store_id":"76e292b2-984d-47d3-a16d-e867f7401bfc","updated_at":"2024-08-30T21:49:40.084Z","isStarred":false},"params":{"questionSlug":"if-fx-left-beginmatrix-a---1-0-ax-a---1-ax2-ax-a-e"}}]}]]

Question: If f(x) = \(\left| \begin{matrix} a & - 1 & 0 \\ ax & a & - 1 \\ ax^{2} & ax & a \end{matrix} \right...

Solution