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_3163.png?top_left_x=532&top_left_y=0&width=532&height=353&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e7e425d76b7ab32ab58","slug":"if-asubrsub-beginpmatrix-r-r---1-r---1-r-endpmatri-1","content":"If A_r = \\(\\begin{pmatrix}\nr & r - 1 \\\\\nr - 1 & r\n\\end{pmatrix}\\) where r is a natural number then\n\n\\|A₁\\| + \\|A₂\\| + \\|A₃\\| + ......+ \\|A₂₀₀₆\\| must be equal to","options":[{"_id":"68a3797e7f15af4716b5d483","text":"2006","sequence":0,"isCorrect":false},{"_id":"68a3797e7f15af4716b5d484","text":"(2006)²","sequence":1,"isCorrect":true},{"_id":"68a3797e7f15af4716b5d485","text":"(2006)³","sequence":2,"isCorrect":false},{"_id":"68a3797e7f15af4716b5d486","text":"2007","sequence":3,"isCorrect":false}],"correct_answer":"(2006)²","explanation":"\\|A_r\\| = r² –(r –1)² = 2r –1\n\nŽ \\|A₁\\| + \\|A₂\\| + ...... + \\|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":"2eecd210-d9a4-4cb5-ba20-f8e0b73f62fa","updated_at":"2024-08-30T21:49:50.501Z","isStarred":false},"params":{"questionSlug":"if-asubrsub-beginpmatrix-r-r---1-r---1-r-endpmatri-1"}}]}]]

Question: If A<sub>r</sub> = \(\begin{pmatrix} r & r - 1 \\ r - 1 & r \end{pmatrix}\) where r is a natural num...

Solution