{"id":2284,"date":"2023-07-22T22:38:26","date_gmt":"2023-07-22T22:38:26","guid":{"rendered":"https:\/\/statorials.org\/pl\/rozwiazac-uklad-rownan-w-r\/"},"modified":"2023-07-22T22:38:26","modified_gmt":"2023-07-22T22:38:26","slug":"rozwiazac-uklad-rownan-w-r","status":"publish","type":"post","link":"https:\/\/statorials.org\/pl\/rozwiazac-uklad-rownan-w-r\/","title":{"rendered":"Jak rozwi\u0105za\u0107 uk\u0142ad r\u00f3wna\u0144 w r (3 przyk\u0142ady)"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">Aby rozwi\u0105za\u0107 uk\u0142ad r\u00f3wna\u0144 w R, mo\u017cemy skorzysta\u0107 z wbudowanej funkcji <b>Solve()<\/b> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Poni\u017csze przyk\u0142ady pokazuj\u0105, jak u\u017cywa\u0107 tych funkcji do rozwi\u0105zywania kilku r\u00f3\u017cnych uk\u0142ad\u00f3w r\u00f3wna\u0144 w R.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Przyk\u0142ad 1: Rozwi\u0105\u017c uk\u0142ad r\u00f3wna\u0144 z dwiema zmiennymi<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Za\u0142\u00f3\u017cmy, \u017ce mamy nast\u0119puj\u0105cy uk\u0142ad r\u00f3wna\u0144 i chcemy rozwi\u0105za\u0107 warto\u015bci x i y:<\/span><\/p>\n<p> <span style=\"color: #000000;\">5x + 4 lata = 35<\/span><\/p>\n<p> <span style=\"color: #000000;\">2x + 6 lat = 36<\/span><\/p>\n<p> <span style=\"color: #000000;\">Poni\u017cszy kod pokazuje, jak u\u017cywa\u0107 funkcji <strong>Solve()<\/strong> w R do rozwi\u0105zywania warto\u015bci x i y:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#define left-hand side of equations\n<\/span>left_matrix &lt;- matrix(c(5, 2, 4, 6), nrow= <span style=\"color: #008000;\">2<\/span> )\n\nleft_matrix\n\n     [,1] [,2]\n[1,] 5 4\n[2,] 2 6\n\n<span style=\"color: #008080;\">#define right-hand side of equations\n<\/span>right_matrix &lt;- matrix(c(35, 36), nrow= <span style=\"color: #008000;\">2<\/span> )\n\nright_matrix\n\n     [,1]\n[1,] 35\n[2,] 36\n\n<span style=\"color: #008080;\">#solve for x and y\n<\/span>solve(left_matrix, right_matrix)  \n\n     [,1]\n[1,] 3\n[2,] 5\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">To m\u00f3wi nam, \u017ce warto\u015b\u0107 x wynosi <strong>3<\/strong> , a warto\u015b\u0107 y wynosi <strong>5<\/strong> .<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Przyk\u0142ad 2: Rozwi\u0105zywanie uk\u0142adu r\u00f3wna\u0144 z trzema zmiennymi<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Za\u0142\u00f3\u017cmy, \u017ce mamy nast\u0119puj\u0105cy uk\u0142ad r\u00f3wna\u0144 i chcemy rozwi\u0105za\u0107 warto\u015bci x, y i z:<\/span><\/p>\n<p> <span style=\"color: #000000;\">4x + 2y + 1z = 34<\/span><\/p>\n<p> <span style=\"color: #000000;\">3x + 5 lat \u2013 2z = 41<\/span><\/p>\n<p> <span style=\"color: #000000;\">2x + 2a + 4z = 30<\/span><\/p>\n<p> <span style=\"color: #000000;\">Poni\u017cszy kod pokazuje, jak u\u017cywa\u0107 funkcji <strong>Solve()<\/strong> w R do rozwi\u0105zywania warto\u015bci x, y i z:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#define left-hand side of equations\n<\/span>left_matrix &lt;- matrix(c(4, 3, 2, 2, 5, 2, 1, -2, 4), nrow= <span style=\"color: #008000;\">3<\/span> )\n\nleft_matrix\n\n     [,1] [,2] [,3]\n[1,] 4 2 1\n[2,] 3 5 -2\n[3,] 2 2 4\n\n<span style=\"color: #008080;\">#define right-hand side of equations\n<\/span>right_matrix &lt;- matrix(c(34, 41, 30), nrow= <span style=\"color: #008000;\">3<\/span> )\n\nright_matrix\n\n     [,1]\n[1,] 34\n[2,] 41\n[3,] 30\n\n<span style=\"color: #008080;\">#solve for x, y, and z\n<\/span>solve(left_matrix, right_matrix) \n\n     [,1]\n[1,] 5\n[2,] 6\n[3,] 2<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">To m\u00f3wi nam, \u017ce warto\u015b\u0107 x wynosi <strong>5<\/strong> , warto\u015b\u0107 y wynosi <strong>6<\/strong> , a warto\u015b\u0107 z wynosi <strong>2<\/strong> .<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Przyk\u0142ad 3: Rozwi\u0105zywanie uk\u0142adu r\u00f3wna\u0144 z czterema zmiennymi<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Za\u0142\u00f3\u017cmy, \u017ce mamy nast\u0119puj\u0105cy uk\u0142ad r\u00f3wna\u0144 i chcemy rozwi\u0105za\u0107 warto\u015bci w, x, y i z:<\/span><\/p>\n<p> <span style=\"color: #000000;\">6w + 2x + 2y + 1z = 37<\/span><\/p>\n<p> <span style=\"color: #000000;\">2w + 1x + 1y + 0z = 14<\/span><\/p>\n<p> <span style=\"color: #000000;\">3s + 2x + 2a + 4z = 28<\/span><\/p>\n<p> <span style=\"color: #000000;\">2w + 0x + 5y + 5z = 28<\/span><\/p>\n<p> <span style=\"color: #000000;\">Poni\u017cszy kod pokazuje, jak u\u017cywa\u0107 funkcji <strong>Solve()<\/strong> w R do rozwi\u0105zywania warto\u015bci w, x, y i z:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#define left-hand side of equations\n<\/span>left_matrix &lt;- matrix(c(6, 2, 3, 2, 2, 1, 2, 0, 2, 1, 2, 5, 1, 0, 4, 5), nrow= <span style=\"color: #008000;\">4<\/span> )\n\nleft_matrix\n\n     [,1] [,2] [,3] [,4]\n[1,] 6 2 2 1\n[2,] 2 1 1 0\n[3,] 3 2 2 4\n[4,] 2 0 5 5\n\n<span style=\"color: #008080;\">#define right-hand side of equations\n<\/span>right_matrix &lt;- matrix(c(37, 14, 28, 28), nrow= <span style=\"color: #008000;\">4<\/span> )\n\nright_matrix\n\n     [,1]\n[1,] 37\n[2,] 14\n[3,] 28\n[4,] 28\n\n<span style=\"color: #008080;\">#solve for w, x, y and z\n<\/span>solve(left_matrix, right_matrix)\n\n     [,1]\n[1,] 4\n[2,] 3\n[3,] 3\n[4,] 1<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">To m\u00f3wi nam, \u017ce warto\u015b\u0107 w wynosi <strong>4<\/strong> , x wynosi <strong>3<\/strong> , y wynosi <strong>3<\/strong> , a z wynosi <strong>1<\/strong> .<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Dodatkowe zasoby<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Poni\u017csze samouczki wyja\u015bniaj\u0105, jak wykonywa\u0107 inne typowe operacje w j\u0119zyku R:<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/pl\/piec-liczb-podsumowanych-w-r\/\" target=\"_blank\" rel=\"noopener\">Jak obliczy\u0107 podsumowanie pi\u0119ciu liczb w R<\/a><br \/> <a href=\"https:\/\/statorials.org\/pl\/tabela-podsumowujaca-w-r\/\" target=\"_blank\" rel=\"noopener\">Jak utworzy\u0107 tabele podsumowuj\u0105ce w R<\/a><br \/> <a href=\"https:\/\/statorials.org\/pl\/wynik-zr\/\" target=\"_blank\" rel=\"noopener\">Jak obliczy\u0107 wyniki Z w R<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Aby rozwi\u0105za\u0107 uk\u0142ad r\u00f3wna\u0144 w R, mo\u017cemy skorzysta\u0107 z wbudowanej funkcji Solve() . Poni\u017csze przyk\u0142ady pokazuj\u0105, jak u\u017cywa\u0107 tych funkcji do rozwi\u0105zywania kilku r\u00f3\u017cnych uk\u0142ad\u00f3w r\u00f3wna\u0144 w R. Przyk\u0142ad 1: Rozwi\u0105\u017c uk\u0142ad r\u00f3wna\u0144 z dwiema zmiennymi Za\u0142\u00f3\u017cmy, \u017ce mamy nast\u0119puj\u0105cy uk\u0142ad r\u00f3wna\u0144 i chcemy rozwi\u0105za\u0107 warto\u015bci x i y: 5x + 4 lata = 35 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-2284","post","type-post","status-publish","format-standard","hentry","category-przewodnik"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Jak rozwi\u0105za\u0107 uk\u0142ad r\u00f3wna\u0144 w R (3 przyk\u0142ady) - Statoriale<\/title>\n<meta name=\"description\" content=\"W tym samouczku wyja\u015bniono, jak rozwi\u0105za\u0107 uk\u0142ad r\u00f3wna\u0144 w j\u0119zyku R, podaj\u0105c kilka przyk\u0142ad\u00f3w.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/pl\/rozwiazac-uklad-rownan-w-r\/\" \/>\n<meta property=\"og:locale\" content=\"pl_PL\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Jak rozwi\u0105za\u0107 uk\u0142ad r\u00f3wna\u0144 w R (3 przyk\u0142ady) - Statoriale\" \/>\n<meta property=\"og:description\" content=\"W tym samouczku wyja\u015bniono, jak rozwi\u0105za\u0107 uk\u0142ad r\u00f3wna\u0144 w j\u0119zyku R, podaj\u0105c kilka przyk\u0142ad\u00f3w.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pl\/rozwiazac-uklad-rownan-w-r\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-22T22:38:26+00:00\" \/>\n<meta name=\"author\" content=\"Benjamin Anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Napisane przez\" \/>\n\t<meta name=\"twitter:data1\" content=\"Benjamin Anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Szacowany czas czytania\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minuty\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/pl\/rozwiazac-uklad-rownan-w-r\/\",\"url\":\"https:\/\/statorials.org\/pl\/rozwiazac-uklad-rownan-w-r\/\",\"name\":\"Jak rozwi\u0105za\u0107 uk\u0142ad r\u00f3wna\u0144 w R (3 przyk\u0142ady) - Statoriale\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pl\/#website\"},\"datePublished\":\"2023-07-22T22:38:26+00:00\",\"dateModified\":\"2023-07-22T22:38:26+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pl\/#\/schema\/person\/6484727a4612df3e69f016c3129c6965\"},\"description\":\"W tym samouczku wyja\u015bniono, jak rozwi\u0105za\u0107 uk\u0142ad r\u00f3wna\u0144 w j\u0119zyku R, podaj\u0105c kilka przyk\u0142ad\u00f3w.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pl\/rozwiazac-uklad-rownan-w-r\/#breadcrumb\"},\"inLanguage\":\"pl-PL\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pl\/rozwiazac-uklad-rownan-w-r\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pl\/rozwiazac-uklad-rownan-w-r\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Dom\",\"item\":\"https:\/\/statorials.org\/pl\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Jak rozwi\u0105za\u0107 uk\u0142ad r\u00f3wna\u0144 w r (3 przyk\u0142ady)\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/pl\/#website\",\"url\":\"https:\/\/statorials.org\/pl\/\",\"name\":\"Statorials\",\"description\":\"Tw\u00f3j przewodnik po kompetencjach statystycznych!\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/pl\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"pl-PL\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/pl\/#\/schema\/person\/6484727a4612df3e69f016c3129c6965\",\"name\":\"Benjamin Anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"pl-PL\",\"@id\":\"https:\/\/statorials.org\/pl\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/statorials.org\/pl\/wp-content\/uploads\/2023\/11\/Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"https:\/\/statorials.org\/pl\/wp-content\/uploads\/2023\/11\/Benjamin-Anderson-96x96.jpg\",\"caption\":\"Benjamin Anderson\"},\"description\":\"Cze\u015b\u0107, jestem Benjamin i jestem emerytowanym profesorem statystyki, kt\u00f3ry zosta\u0142 oddanym nauczycielem Statorials. 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