{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-05-26T00:16:20.000Z","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":"2026-05-26T00:00:00.000Z","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":978,"title":"Backward Substitution","description":"Solve a upper triangular linear set of equations as described in the following link: http://www.people.virginia.edu/~teh1m/cody/backsub1.pdf","description_html":"\u003cp\u003eSolve a upper triangular linear set of equations as described in the following link: \u003ca href=\"http://www.people.virginia.edu/~teh1m/cody/backsub1.pdf\"\u003ehttp://www.people.virginia.edu/~teh1m/cody/backsub1.pdf\u003c/a\u003e\u003c/p\u003e","function_template":"function [x] = my_backsub(A,b)\r\nx = b;\r\nend\r\n","test_suite":"%%\r\nA=[2     3     7; 0     5     8; 0     0     9];\r\nb=[12; 13; 9];\r\ny_correct = [1; 1; 1];\r\nassert(isequal(my_backsub(A,b),y_correct))\r\n%%\r\nA=[2     3     7; 0     5     8; 1     0     9];\r\nb=[12; 13; 9];\r\ny_correct = [inf];\r\nassert(isequal(my_backsub(A,b),y_correct))\r\n%%\r\nA=[7.9200    9.5900    6.5600\r\n         0    8.4900    9.3400\r\n         0         0    7.4300];\r\nb=[   66.3400\r\n   48.4000\r\n   52.0100];\r\ny_correct = [5; -2; 7];\r\nassert(isequal(my_backsub(A,b),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":2640,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":37,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2012-10-08T15:44:25.000Z","updated_at":"2026-05-26T06:15:57.000Z","published_at":"2012-10-10T16:22:17.000Z","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 version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSolve a upper triangular linear set of equations as described in the following link:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.people.virginia.edu/~teh1m/cody/backsub1.pdf\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttp://www.people.virginia.edu/~teh1m/cody/backsub1.pdf\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\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":{"problems":[{"id":978,"title":"Backward Substitution","description":"Solve a upper triangular linear set of equations as described in the following link: http://www.people.virginia.edu/~teh1m/cody/backsub1.pdf","description_html":"\u003cp\u003eSolve a upper triangular linear set of equations as described in the following link: \u003ca href=\"http://www.people.virginia.edu/~teh1m/cody/backsub1.pdf\"\u003ehttp://www.people.virginia.edu/~teh1m/cody/backsub1.pdf\u003c/a\u003e\u003c/p\u003e","function_template":"function [x] = my_backsub(A,b)\r\nx = b;\r\nend\r\n","test_suite":"%%\r\nA=[2     3     7; 0     5     8; 0     0     9];\r\nb=[12; 13; 9];\r\ny_correct = [1; 1; 1];\r\nassert(isequal(my_backsub(A,b),y_correct))\r\n%%\r\nA=[2     3     7; 0     5     8; 1     0     9];\r\nb=[12; 13; 9];\r\ny_correct = [inf];\r\nassert(isequal(my_backsub(A,b),y_correct))\r\n%%\r\nA=[7.9200    9.5900    6.5600\r\n         0    8.4900    9.3400\r\n         0         0    7.4300];\r\nb=[   66.3400\r\n   48.4000\r\n   52.0100];\r\ny_correct = [5; -2; 7];\r\nassert(isequal(my_backsub(A,b),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":2640,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":37,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2012-10-08T15:44:25.000Z","updated_at":"2026-05-26T06:15:57.000Z","published_at":"2012-10-10T16:22:17.000Z","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 version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSolve a upper triangular linear set of equations as described in the following link:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.people.virginia.edu/~teh1m/cody/backsub1.pdf\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttp://www.people.virginia.edu/~teh1m/cody/backsub1.pdf\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\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\"}]}"}],"errors":[],"facets":[[],[{"value":"easy","count":1,"selected":false}]],"term":"tag:\"back substitution\"","page":1,"per_page":50,"sort":"map(difficulty_value,0,0,999) asc"}}