{"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":42988,"title":"Linear system of equations","description":"Solve the system of equations in three variables.","description_html":"\u003cp\u003eSolve the system of equations in three variables.\u003c/p\u003e","function_template":"function y = lin_eqns(A,b)\r\n  y = b;\r\nend","test_suite":"%%\r\nA=[1 1 1;2 4 8;3 9 27];\r\nb=[1;2;3];\r\ny_correct = [1;0;0];\r\ntol = 1e-14;\r\nassert(norm(lin_eqns(A,b)-y_correct) \u003c tol)\r\n\r\n%%\r\nA=[2 1 -2;1 -1 -1;1 1 3];\r\nb=[3;0;12];\r\ny_correct = [3.5;1;2.5];\r\ntol = 1e-14;\r\nassert(norm(lin_eqns(A,b)-y_correct) \u003c tol)\r\n\r\n%%\r\nA=[1 0 0;0 1 0;0 0 1];\r\nb=[1e6;1e7;1e8];\r\ny_correct = [1e6;1e7;1e8];\r\ntol = 1e-9;\r\nassert(norm(lin_eqns(A,b)-y_correct) \u003c tol)\r\n\r\n%%\r\nA=[1 0 1;0 -3 1;2 1 3];\r\nb=[6;7;15];\r\ny_correct = [2;-1;4];\r\ntol = 1e-14;\r\nassert(norm(lin_eqns(A,b)-y_correct) \u003c tol)\r\n","published":true,"deleted":false,"likes_count":13,"comments_count":1,"created_by":91311,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":468,"test_suite_updated_at":"2016-10-02T01:16:37.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2016-09-19T10:00:24.000Z","updated_at":"2026-03-29T20:48:31.000Z","published_at":"2016-09-19T10:00:24.000Z","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\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"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\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 the system of equations in three variables.\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\"}]}"},{"id":446,"title":"Solve the set of simultaneous linear equations ","description":"Given this pair of simultaneous linear equations:\r\n\r\n2x + 3y = 23\r\n\r\n3x + 4y = 32\r\n\r\nFind the solution set (x,y)","description_html":"\u003cp\u003eGiven this pair of simultaneous linear equations:\u003c/p\u003e\u003cp\u003e2x + 3y = 23\u003c/p\u003e\u003cp\u003e3x + 4y = 32\u003c/p\u003e\u003cp\u003eFind the solution set (x,y)\u003c/p\u003e","function_template":"function x = solveSimul(A,b)\r\n  x = A + b;\r\nend","test_suite":"%% test 1\r\nA = [2 3; 3 4]; b = [23; 32];\r\nx_correct = [4;5];\r\nassert(isequal(solveSimul(A,b),x_correct))\r\n\r\n%% test 2\r\nA = [2 3; 3 4]; b = [23; 36];\r\nx_correct = [16;-3];\r\nassert(isequal(solveSimul(A,b),x_correct))\r\n\r\n%% test 3\r\nA = [2 3; 3 4]; b = [23; 43];\r\nx_correct = [37;-17];\r\nassert(isequal(solveSimul(A,b),x_correct))\r\n\r\n%% test 4\r\nA = [2 3; 3 4]; b = [23; 49];\r\nx_correct = [55;-29];\r\nassert(isequal(solveSimul(A,b),x_correct))\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":1,"created_by":1103,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":504,"test_suite_updated_at":"2012-03-17T22:41:43.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-03-04T08:34:50.000Z","updated_at":"2026-03-29T20:51:21.000Z","published_at":"2012-03-17T22:42:59.000Z","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\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"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\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\u003eGiven this pair of simultaneous linear equations:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e2x + 3y = 23\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e3x + 4y = 32\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the solution set (x,y)\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\"}]}"},{"id":389,"title":"Column norms of a matrix","description":"Given a matrix M, return a vector y such that for each k\r\n\r\n    y(k)=norm(M(:,k))\r\n\r\n(y(k) is the Euclidean norm of the k-th column of M)\r\n\r\nEDIT: changed the test case so that proper handling of complex values is required.","description_html":"\u003cp\u003eGiven a matrix M, return a vector y such that for each k\u003c/p\u003e\u003cpre\u003e    y(k)=norm(M(:,k))\u003c/pre\u003e\u003cp\u003e(y(k) is the Euclidean norm of the k-th column of M)\u003c/p\u003e\u003cp\u003eEDIT: changed the test case so that proper handling of complex values is required.\u003c/p\u003e","function_template":"function y = your_fcn_name(M)\r\n  y = M;\r\nend","test_suite":"%%\r\nM = [1 2 3; 4 5 6; 7 8 9+2i];\r\nfor k=1:size(M,2)\r\n  y_correct(k)=norm(M(:,k));\r\nend\r\nassert(isequal(your_fcn_name(M),y_correct))\r\n","published":true,"deleted":false,"likes_count":9,"comments_count":1,"created_by":1258,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":569,"test_suite_updated_at":"2012-02-24T14:50:55.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-02-23T09:33:39.000Z","updated_at":"2026-03-29T18:47:57.000Z","published_at":"2012-02-24T14:50:55.000Z","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\u003eGiven a matrix M, return a vector y such that for each k\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[    y(k)=norm(M(:,k))]]\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\u003e(y(k) is the Euclidean norm of the k-th column of M)\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\u003eEDIT: changed the test case so that proper handling of complex values is required.\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":42988,"title":"Linear system of equations","description":"Solve the system of equations in three variables.","description_html":"\u003cp\u003eSolve the system of equations in three variables.\u003c/p\u003e","function_template":"function y = lin_eqns(A,b)\r\n  y = b;\r\nend","test_suite":"%%\r\nA=[1 1 1;2 4 8;3 9 27];\r\nb=[1;2;3];\r\ny_correct = [1;0;0];\r\ntol = 1e-14;\r\nassert(norm(lin_eqns(A,b)-y_correct) \u003c tol)\r\n\r\n%%\r\nA=[2 1 -2;1 -1 -1;1 1 3];\r\nb=[3;0;12];\r\ny_correct = [3.5;1;2.5];\r\ntol = 1e-14;\r\nassert(norm(lin_eqns(A,b)-y_correct) \u003c tol)\r\n\r\n%%\r\nA=[1 0 0;0 1 0;0 0 1];\r\nb=[1e6;1e7;1e8];\r\ny_correct = [1e6;1e7;1e8];\r\ntol = 1e-9;\r\nassert(norm(lin_eqns(A,b)-y_correct) \u003c tol)\r\n\r\n%%\r\nA=[1 0 1;0 -3 1;2 1 3];\r\nb=[6;7;15];\r\ny_correct = [2;-1;4];\r\ntol = 1e-14;\r\nassert(norm(lin_eqns(A,b)-y_correct) \u003c tol)\r\n","published":true,"deleted":false,"likes_count":13,"comments_count":1,"created_by":91311,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":468,"test_suite_updated_at":"2016-10-02T01:16:37.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2016-09-19T10:00:24.000Z","updated_at":"2026-03-29T20:48:31.000Z","published_at":"2016-09-19T10:00:24.000Z","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\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"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\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 the system of equations in three variables.\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\"}]}"},{"id":446,"title":"Solve the set of simultaneous linear equations ","description":"Given this pair of simultaneous linear equations:\r\n\r\n2x + 3y = 23\r\n\r\n3x + 4y = 32\r\n\r\nFind the solution set (x,y)","description_html":"\u003cp\u003eGiven this pair of simultaneous linear equations:\u003c/p\u003e\u003cp\u003e2x + 3y = 23\u003c/p\u003e\u003cp\u003e3x + 4y = 32\u003c/p\u003e\u003cp\u003eFind the solution set (x,y)\u003c/p\u003e","function_template":"function x = solveSimul(A,b)\r\n  x = A + b;\r\nend","test_suite":"%% test 1\r\nA = [2 3; 3 4]; b = [23; 32];\r\nx_correct = [4;5];\r\nassert(isequal(solveSimul(A,b),x_correct))\r\n\r\n%% test 2\r\nA = [2 3; 3 4]; b = [23; 36];\r\nx_correct = [16;-3];\r\nassert(isequal(solveSimul(A,b),x_correct))\r\n\r\n%% test 3\r\nA = [2 3; 3 4]; b = [23; 43];\r\nx_correct = [37;-17];\r\nassert(isequal(solveSimul(A,b),x_correct))\r\n\r\n%% test 4\r\nA = [2 3; 3 4]; b = [23; 49];\r\nx_correct = [55;-29];\r\nassert(isequal(solveSimul(A,b),x_correct))\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":1,"created_by":1103,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":504,"test_suite_updated_at":"2012-03-17T22:41:43.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-03-04T08:34:50.000Z","updated_at":"2026-03-29T20:51:21.000Z","published_at":"2012-03-17T22:42:59.000Z","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\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"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\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\u003eGiven this pair of simultaneous linear equations:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e2x + 3y = 23\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e3x + 4y = 32\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the solution set 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each k\u003c/p\u003e\u003cpre\u003e    y(k)=norm(M(:,k))\u003c/pre\u003e\u003cp\u003e(y(k) is the Euclidean norm of the k-th column of M)\u003c/p\u003e\u003cp\u003eEDIT: changed the test case so that proper handling of complex values is required.\u003c/p\u003e","function_template":"function y = your_fcn_name(M)\r\n  y = M;\r\nend","test_suite":"%%\r\nM = [1 2 3; 4 5 6; 7 8 9+2i];\r\nfor k=1:size(M,2)\r\n  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