test","extracted_subject":"MATH","extracted_chapter":"DETERMINANTS AND MATRICES","extracted_topic":"SPECIAL TYPES OF MATRICES, TRANSPOSE, ADJOINT AND INVERSE OF MATRICES","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_3162.png?top_left_x=532&top_left_y=1547&width=532&height=324&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e7e425d76b7ab32ab57","slug":"if-asubrsub-beginpmatrix-r-r---1-r---1-rendpmatrix","content":"If A_r = \\(\\begin{pmatrix}\nr & r - 1 \\\\\nr - 1 & r\\end{pmatrix}\\) where r Ī N then the value of\n\n\\|A₁\\| + \\|A₂\\| + \\|A₃\\| + ………..+\\|A₂₀₀₆\\| is –","options":[{"_id":"68a38b597f15af4716b8b539","text":"2006","sequence":0,"isCorrect":false},{"_id":"68a38b597f15af4716b8b53a","text":"(2006)²","sequence":1,"isCorrect":true},{"_id":"68a38b597f15af4716b8b53b","text":"(2006)³","sequence":2,"isCorrect":false},{"_id":"68a38b597f15af4716b8b53c","text":"2007","sequence":3,"isCorrect":false}],"correct_answer":"(2006)²","explanation":"\\|A_r\\| = 2r – 1\n\n\\|A₁\\| + \\|A₂\\| + \\|A₃\\| + ………..+\\|A₂₀₀₆\\|\n\n= \\(\\sum_{r = 1}^{2006}(2r - 1)\\) = (2006)²","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:50.501Z","__v":0,"vector_store_id":"47b0ad4a-090a-4842-88ff-6af7ef88524c","updated_at":"2024-08-30T21:49:50.501Z","isStarred":false},"params":{"questionSlug":"if-asubrsub-beginpmatrix-r-r---1-r---1-rendpmatrix"}}]}]]

Question: If A<sub>r</sub> = \(\begin{pmatrix} r & r - 1 \\ r - 1 & r\end{pmatrix}\) where r Ī N then the valu...

Solution