{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":2813,"title":"Create a block diagonal matrix","description":"A block diagonal matrix is a square matrix that can be written as\r\n\r\n   A = [a  0  0  0\r\n        0  b  0  0\r\n        0  0  c  0\r\n        0  0  0 ...]\r\n\r\nwhere |a|, |b|, |c| etc. are all square matrices.\r\n\r\nConstruct |A| such that\r\n\r\n   A = [a  0  0  0\r\n        0  a  0  0\r\n        0  0  a  0\r\n        0  0  0 ...]\r\n\r\nwhere |a| is allowed to be non-square or empty and occurs |n| times. |n| is always an integer greater than or equal to 0.\r\n\r\n*Examples:*\r\n\r\n   a = [1 2 3], n = 3\r\n\r\ngives\r\n\r\n   A = [1 2 3 0 0 0 0 0 0\r\n        0 0 0 1 2 3 0 0 0\r\n        0 0 0 0 0 0 1 2 3]\r\n","description_html":"\u003cp\u003eA block diagonal matrix is a square matrix that can be written as\u003c/p\u003e\u003cpre\u003e   A = [a  0  0  0\r\n        0  b  0  0\r\n        0  0  c  0\r\n        0  0  0 ...]\u003c/pre\u003e\u003cp\u003ewhere \u003ctt\u003ea\u003c/tt\u003e, \u003ctt\u003eb\u003c/tt\u003e, \u003ctt\u003ec\u003c/tt\u003e etc. are all square matrices.\u003c/p\u003e\u003cp\u003eConstruct \u003ctt\u003eA\u003c/tt\u003e such that\u003c/p\u003e\u003cpre\u003e   A = [a  0  0  0\r\n        0  a  0  0\r\n        0  0  a  0\r\n        0  0  0 ...]\u003c/pre\u003e\u003cp\u003ewhere \u003ctt\u003ea\u003c/tt\u003e is allowed to be non-square or empty and occurs \u003ctt\u003en\u003c/tt\u003e times. \u003ctt\u003en\u003c/tt\u003e is always an integer greater than or equal to 0.\u003c/p\u003e\u003cp\u003e\u003cb\u003eExamples:\u003c/b\u003e\u003c/p\u003e\u003cpre\u003e   a = [1 2 3], n = 3\u003c/pre\u003e\u003cp\u003egives\u003c/p\u003e\u003cpre\u003e   A = [1 2 3 0 0 0 0 0 0\r\n        0 0 0 1 2 3 0 0 0\r\n        0 0 0 0 0 0 1 2 3]\u003c/pre\u003e","function_template":"function A = block_diagonal(a,n)\r\n  A = a^n;\r\nend","test_suite":"%%\r\na = [1 2 3];\r\nn = 3;\r\nA_correct = [1 2 3 0 0 0 0 0 0; 0 0 0 1 2 3 0 0 0; 0 0 0 0 0 0 1 2 3];\r\nassert(isequal(block_diagonal(a,n),A_correct))\r\n\r\n%%\r\na = [];\r\nn = 3;\r\nA_correct = [];\r\nassert(isequal(block_diagonal(a,n),A_correct))\r\n\r\n%%\r\na = [1 2 -3]';\r\nn = 0;\r\nA_correct = [];\r\nassert(isequal(block_diagonal(a,n),A_correct))\r\n\r\n%%\r\na = [3 -2]';\r\nn = 4;\r\nA_correct = [3 -2 0 0 0 0 0 0; 0 0 3 -2 0 0 0 0; 0 0 0 0 3 -2 0 0; 0 0 0 0 0 0 3 -2]';\r\nassert(isequal(block_diagonal(a,n),A_correct))\r\n\r\n%%\r\na = 6;\r\nn = 23;\r\nA_correct = a*eye(n);\r\nassert(isequal(block_diagonal(a,n),A_correct))\r\n\r\n%%\r\na = magic(5);\r\nn = 2;\r\nA_correct = [a zeros(5); zeros(5) a];\r\nassert(isequal(block_diagonal(a,n),A_correct))\r\n\r\n%%\r\na = randi(100,13,8);\r\nn = 1;\r\nA_correct = a;\r\nassert(isequal(block_diagonal(a,n),A_correct))\r\n","published":true,"deleted":false,"likes_count":5,"comments_count":2,"created_by":33611,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":168,"test_suite_updated_at":"2015-01-06T13:07:33.000Z","rescore_all_solutions":false,"group_id":31,"created_at":"2015-01-06T12:10:41.000Z","updated_at":"2026-03-04T16:27:51.000Z","published_at":"2015-01-06T13:05:19.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml 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\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e such that\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[   A = [a  0  0  0\\n        0  a  0  0\\n        0  0  a  0\\n        0  0  0 ...]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is allowed to be non-square or empty and occurs\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e times.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is always an integer greater than or equal to 0.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[   a = [1 2 3], n = 3]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003egives\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[   A = [1 2 3 0 0 0 0 0 0\\n        0 0 0 1 2 3 0 0 0\\n        0 0 0 0 0 0 1 2 3]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":2813,"title":"Create a block diagonal matrix","description":"A block diagonal matrix is a square matrix that can be written as\r\n\r\n   A = [a  0  0  0\r\n        0  b  0  0\r\n        0  0  c  0\r\n        0  0  0 ...]\r\n\r\nwhere |a|, |b|, |c| etc. are all square matrices.\r\n\r\nConstruct |A| such that\r\n\r\n   A = [a  0  0  0\r\n        0  a  0  0\r\n        0  0  a  0\r\n        0  0  0 ...]\r\n\r\nwhere |a| is allowed to be non-square or empty and occurs |n| times. |n| is always an integer greater than or equal to 0.\r\n\r\n*Examples:*\r\n\r\n   a = [1 2 3], n = 3\r\n\r\ngives\r\n\r\n   A = [1 2 3 0 0 0 0 0 0\r\n        0 0 0 1 2 3 0 0 0\r\n        0 0 0 0 0 0 1 2 3]\r\n","description_html":"\u003cp\u003eA block diagonal matrix is a square matrix that can be written as\u003c/p\u003e\u003cpre\u003e   A = [a  0  0  0\r\n        0  b  0  0\r\n        0  0  c  0\r\n        0  0  0 ...]\u003c/pre\u003e\u003cp\u003ewhere \u003ctt\u003ea\u003c/tt\u003e, \u003ctt\u003eb\u003c/tt\u003e, \u003ctt\u003ec\u003c/tt\u003e etc. are all square matrices.\u003c/p\u003e\u003cp\u003eConstruct \u003ctt\u003eA\u003c/tt\u003e such that\u003c/p\u003e\u003cpre\u003e   A = [a  0  0  0\r\n        0  a  0  0\r\n        0  0  a  0\r\n        0  0  0 ...]\u003c/pre\u003e\u003cp\u003ewhere \u003ctt\u003ea\u003c/tt\u003e is allowed to be non-square or empty and occurs \u003ctt\u003en\u003c/tt\u003e times. \u003ctt\u003en\u003c/tt\u003e is always an integer greater than or equal to 0.\u003c/p\u003e\u003cp\u003e\u003cb\u003eExamples:\u003c/b\u003e\u003c/p\u003e\u003cpre\u003e   a = [1 2 3], n = 3\u003c/pre\u003e\u003cp\u003egives\u003c/p\u003e\u003cpre\u003e   A = [1 2 3 0 0 0 0 0 0\r\n        0 0 0 1 2 3 0 0 0\r\n        0 0 0 0 0 0 1 2 3]\u003c/pre\u003e","function_template":"function A = block_diagonal(a,n)\r\n  A = a^n;\r\nend","test_suite":"%%\r\na = [1 2 3];\r\nn = 3;\r\nA_correct = [1 2 3 0 0 0 0 0 0; 0 0 0 1 2 3 0 0 0; 0 0 0 0 0 0 1 2 3];\r\nassert(isequal(block_diagonal(a,n),A_correct))\r\n\r\n%%\r\na = [];\r\nn = 3;\r\nA_correct = [];\r\nassert(isequal(block_diagonal(a,n),A_correct))\r\n\r\n%%\r\na = [1 2 -3]';\r\nn = 0;\r\nA_correct = [];\r\nassert(isequal(block_diagonal(a,n),A_correct))\r\n\r\n%%\r\na = [3 -2]';\r\nn = 4;\r\nA_correct = [3 -2 0 0 0 0 0 0; 0 0 3 -2 0 0 0 0; 0 0 0 0 3 -2 0 0; 0 0 0 0 0 0 3 -2]';\r\nassert(isequal(block_diagonal(a,n),A_correct))\r\n\r\n%%\r\na = 6;\r\nn = 23;\r\nA_correct = a*eye(n);\r\nassert(isequal(block_diagonal(a,n),A_correct))\r\n\r\n%%\r\na = magic(5);\r\nn = 2;\r\nA_correct = [a zeros(5); zeros(5) a];\r\nassert(isequal(block_diagonal(a,n),A_correct))\r\n\r\n%%\r\na = randi(100,13,8);\r\nn = 1;\r\nA_correct = a;\r\nassert(isequal(block_diagonal(a,n),A_correct))\r\n","published":true,"deleted":false,"likes_count":5,"comments_count":2,"created_by":33611,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":168,"test_suite_updated_at":"2015-01-06T13:07:33.000Z","rescore_all_solutions":false,"group_id":31,"created_at":"2015-01-06T12:10:41.000Z","updated_at":"2026-03-04T16:27:51.000Z","published_at":"2015-01-06T13:05:19.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml 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