st","extracted_subject":"MATH","extracted_chapter":"DETERMINANTS AND MATRICES","extracted_topic":"TYPES OF MATRICES, ALGEBRA OF MATRICES","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_3162.png?top_left_x=1064&top_left_y=830&width=532&height=308&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e7e425d76b7ab32ab50","slug":"matrix-msubrsub-is-defined-as-msubrsub-eginbmatrix","content":"Matrix M_r is defined as M_r =\\(\begin{bmatrix}\nr & r–1 \\\nr–1 & r \\\\end{bmatrix}\\), r Ī N. Then\ndet. (M₁) + det.(M₂) + ........... + det.(M₂₀₀₉) = ?","options":[{"_id":"68a539c77f15af4716cd3681","text":"2009","sequence":0,"isCorrect":false},{"_id":"68a539c77f15af4716cd3682","text":"(2009)²","sequence":1,"isCorrect":true},{"_id":"68a539c77f15af4716cd3683","text":"(2009)³","sequence":2,"isCorrect":false},{"_id":"68a539c77f15af4716cd3684","text":"None of these","sequence":3,"isCorrect":false}],"correct_answer":"(2009)²","explanation":"det.(M_r) = r² – (r –1)² = 2r –1\n\n\\(\\sum_{r = 1}^{2009}{(2r–1)}\\) = 2 × \\(\\left( \\frac{2009 \\times 2010}{2} \\right)\\) – 2009\n\n= (2009) × (2009) = (2009)²","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:50.500Z","__v":0,"vector_store_id":"9ae8a9f0-18ac-4c00-a848-fd9169bb7fc3","updated_at":"2024-08-30T21:49:50.500Z","isStarred":false},"params":{"questionSlug":"matrix-msubrsub-is-defined-as-msubrsub-eginbmatrix"}}]}]]

Question: Matrix M<sub>r</sub> is defined as M<sub>r</sub> =\(egin{bmatrix} r & r–1 \ r–1 & r \\end{bmatrix}\...

Solution

Question: Matrix M<sub>r</sub> is defined as M<sub>r</sub> =\(egin{bmatrix} r & r–1 \ r–1 & r \\end{bmatrix}\...