{"id":317,"date":"2026-10-04T09:33:26","date_gmt":"2026-10-04T08:33:26","guid":{"rendered":"https:\/\/wpcalc.com\/pl\/matematyka\/wartosci-wlasne-wektory-wlasne-2x2\/"},"modified":"2026-10-04T09:33:26","modified_gmt":"2026-10-04T08:33:26","slug":"wartosci-wlasne-wektory-wlasne-2x2","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/pl\/matematyka\/wartosci-wlasne-wektory-wlasne-2x2\/","title":{"rendered":"Kalkulator warto\u015bci w\u0142asnych i wektor\u00f3w w\u0142asnych macierzy 2\u00d72"},"content":{"rendered":"<section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 id=\"calculator-title\" class=\"text-lg font-display font-bold\">2\u00d72 Matrix Eigenvalues and Eigenvectors Solver<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"317\" data-favorite-title=\"Warto\u015bci w\u0142asne i wektory w\u0142asne 2\u00d72\" data-favorite-url=\"https:\/\/wpcalc.com\/pl\/matematyka\/wartosci-wlasne-wektory-wlasne-2x2\/\" data-favorite-excerpt=\"Wprowad\u017a cztery elementy macierzy 2\u00d72, aby otrzyma\u0107 jej warto\u015bci w\u0142asne i wektory w\u0142asne, a tak\u017ce wyznacznik, \u015blad i wielomian charakterystyczny wraz z pe\u0142nym rozwi\u0105zaniem krok po kroku.\" aria-label=\"Dodaj do ulubionych\" data-favorite-icon=\"icon icon-algebra\">\n    <span class=\"icon icon-shape-star-empty\" aria-hidden=\"true\"><\/span>\n  <\/button>\n  <div class=\"calcdash-favorite__tip\" aria-hidden=\"true\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n  <span class=\"sr-only\" role=\"status\" id=\"favorite-status\"><\/span>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/pl\/matematyka\/wartosci-wlasne-wektory-wlasne-2x2\/\" method=\"POST\" class=\"calculator\" id=\"calculator-317\" data-post=\"317\"><fieldset class=\"fieldset-input\"><legend class=\"sr-only\">Pola danych<\/legend><div class=\"field has-term\" id=\"input-1\"><label for=\"field-1\">a\u2081\u2081<\/label><div class=\"term\">a11<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"a\" id=\"field-1\" aria-describedby=\"calc-info-1\" step=\"any\" value=\"4\"\/><small id=\"calc-info-1\">Element macierzy w wierszu 1, kolumnie 1<\/small><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-2\">a\u2081\u2082<\/label><div class=\"term\">a12<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"a\" id=\"field-2\" aria-describedby=\"calc-info-2\" step=\"any\" value=\"2\"\/><small id=\"calc-info-2\">Element macierzy w wierszu 1, kolumnie 2<\/small><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-3\">a\u2082\u2081<\/label><div class=\"term\">a21<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"a\" id=\"field-3\" aria-describedby=\"calc-info-3\" step=\"any\" value=\"1\"\/><small id=\"calc-info-3\">Element macierzy w wierszu 2, kolumnie 1<\/small><\/div><div class=\"field has-term\" id=\"input-4\"><label for=\"field-4\">a\u2082\u2082<\/label><div class=\"term\">a22<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"a\" id=\"field-4\" aria-describedby=\"calc-info-4\" step=\"any\" value=\"3\"\/><small id=\"calc-info-4\">Element macierzy w wierszu 2, kolumnie 2<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Przelicz ponownie\" id=\"calculate-button\" data-post=\"317\">Oblicz<\/button><button type=\"reset\">Wyczy\u015b\u0107<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Obliczaj automatycznie<\/label><small>Po w\u0142\u0105czeniu wynik aktualizuje si\u0119 automatycznie po zmianie dowolnej warto\u015bci.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> Twoje wyniki<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>|A| \u2014 Wyznacznik macierzy<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Kopiuj wynik\" aria-label=\"Kopiuj wynik\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-2\"><span class=\"field-title\"><span>\u015alad A \u2014 Suma element\u00f3w na przek\u0105tnej<\/span><\/span><span class=\"field-value\" id=\"result-2\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Kopiuj wynik\" aria-label=\"Kopiuj wynik\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-3\"><span class=\"field-title\"><span>Macierz zdegenerowana (A \u2212 c\u00d7I)<\/span><\/span><span class=\"field-value\" id=\"result-3\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Kopiuj wynik\" aria-label=\"Kopiuj wynik\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-4\"><span class=\"field-title\"><span>|A \u2212 c\u00d7I| \u2014 Wielomian charakterystyczny<\/span><\/span><span class=\"field-value\" id=\"result-4\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Kopiuj wynik\" aria-label=\"Kopiuj wynik\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-5\"><span class=\"field-title\"><span>Warto\u015b\u0107 w\u0142asna \u03bb\u2081<\/span><\/span><span class=\"field-value\" id=\"result-5\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Kopiuj wynik\" aria-label=\"Kopiuj wynik\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-6\"><span class=\"field-title\"><span>Warto\u015b\u0107 w\u0142asna \u03bb\u2082<\/span><\/span><span class=\"field-value\" id=\"result-6\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Kopiuj wynik\" aria-label=\"Kopiuj wynik\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-7\"><span class=\"field-title\"><span>Wektor w\u0142asny dla \u03bb\u2081 (x\u2081, x\u2082)<\/span><\/span><span class=\"field-value\" id=\"result-7\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Kopiuj wynik\" aria-label=\"Kopiuj wynik\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-8\"><span class=\"field-title\"><span>Wektor w\u0142asny dla \u03bb\u2082 (x\u2081, x\u2082)<\/span><\/span><span class=\"field-value\" id=\"result-8\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Kopiuj wynik\" aria-label=\"Kopiuj wynik\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><\/div><div class=\"result-actions\"><button type=\"button\" class=\"copy-link\"><svg viewBox=\"0 0 20 20\" fill=\"currentColor\" aria-hidden=\"true\"><path d=\"M12.232 4.232a2.5 2.5 0 0 1 3.536 3.536l-1.225 1.224a.75.75 0 0 0 1.061 1.06l1.224-1.224a4 4 0 0 0-5.656-5.656l-3 3a4 4 0 0 0 .225 5.865.75.75 0 0 0 .977-1.138 2.5 2.5 0 0 1-.142-3.667l3-3Z\"\/><path d=\"M11.603 7.963a.75.75 0 0 0-.977 1.138 2.5 2.5 0 0 1 .142 3.667l-3 3a2.5 2.5 0 0 1-3.536-3.536l1.225-1.224a.75.75 0 0 0-1.061-1.06l-1.224 1.224a4 4 0 1 0 5.656 5.656l3-3a4 4 0 0 0-.225-5.865Z\"\/><\/svg><span class=\"copy-link__text\">Kopiuj link do tego obliczenia<\/span><\/button><span class=\"sr-only\" role=\"status\" id=\"copy-link-status\"><\/span><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Zostaw komentarz<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"317\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">Jak oceniasz ten wynik?<\/p><div role=\"group\" aria-labelledby=\"calc-reactions-title\" class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"like\"><span class=\"reaction-count\" data-reaction-count=\"like\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">Lubi\u0119 to <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"helpful\"><span class=\"reaction-count\" data-reaction-count=\"helpful\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">Pomocne <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"confused\"><span class=\"reaction-count\" data-reaction-count=\"confused\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Niejasne <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"disappointed\"><span class=\"reaction-count\" data-reaction-count=\"disappointed\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">Rozczarowanie <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\u274c <\/span><span class=\"reaction-description font-medium\">Niedok\u0142adne <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><div class=\"calcdash-ad not-prose calcdash-ad--calc_result calcdash-ad--in-article\"><ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-1721569815777345\" data-ad-slot=\"6317458308\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\"><\/ins><script>(adsbygoogle = window.adsbygoogle || []).push({});<\/script><\/div>\n<style id=\"wpcoderpro-inline-1\">.formula-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>Eigenvalues and Eigenvectors Formula for 2\u00d72 Matrix<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Wz\u00f3r<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n\\[ \\det(A - \\lambda I) = 0 \\\\ (A - \\lambda I)\\vec{v} = \\vec{0} \\\\ \\det\\begin{bmatrix} a - \\lambda &amp; b \\\\ c &amp; d - \\lambda \\end{bmatrix} = (a-\\lambda)(d-\\lambda) - bc = 0 \\\\ \\lambda_{1,2} = \\frac{\\operatorname{tr}(A) \\pm \\sqrt{\\operatorname{tr}(A)^2 - 4\\det(A)}}{2} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Gdzie:<\/strong><\/p>\n<ul>\n<li>\\( A = \\begin{bmatrix} a &amp; b \\\\ c &amp; d \\end{bmatrix} \\) \u2014 macierz 2\u00d72<\/li>\n<li>\\( \\lambda \\) \u2014 warto\u015bci w\u0142asne (pierwiastki r\u00f3wnania charakterystycznego)<\/li>\n<li>\\( \\vec{v} \\) \u2014 odpowiadaj\u0105ce im wektory w\u0142asne, wyznaczane przez rozwi\u0105zanie uk\u0142adu \\( (A - \\lambda I)\\vec{v} = \\vec{0} \\)<\/li>\n<li>\\( \\operatorname{tr}(A) = a + d \\) \u2014 \u015blad macierzy, a \\( \\det(A) = ad - bc \\) \u2014 wyznacznik<\/li>\n<\/ul>\n<p>Pierwsze r\u00f3wnanie definiuje wielomian charakterystyczny \\( \\lambda^2 - \\operatorname{tr}(A)\\lambda + \\det(A) = 0 \\). Jego rozwi\u0105zanie (zwyk\u0142ego r\u00f3wnania kwadratowego) daje obie warto\u015bci w\u0142asne, a ka\u017cda warto\u015b\u0107 w\u0142asna pozwala nast\u0119pnie wyznaczy\u0107 wektor w\u0142asny z uk\u0142adu jednorodnego \\( (A - \\lambda I)\\vec{v} = \\vec{0} \\).<\/p>\n<p>\r\n<\/section>\n<style id=\"wpcoderpro-inline-2\">.calculation-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section id=\"calculation\" class=\"calculation-box\" aria-labelledby=\"calculation-title\">\r\n\t<div id=\"calculation-title\" class=\"not-prose font-display\"><span class=\"icon icon-unordered-list\" aria-hidden=\"true\"><\/span><h2>Eigenvalues and Eigenvectors 2\u00d72 \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Przyk\u0142ad:<\/strong> znajd\u017a warto\u015bci w\u0142asne i wektory w\u0142asne macierzy<\/p>\n<p>\\[ A = \\begin{bmatrix} 4 &amp; 2 \\\\ 1 &amp; 3 \\end{bmatrix} \\]<\/p>\n<p>Krok 1 \u2014 \u015blad i wyznacznik: \\( \\operatorname{tr}(A) = 4 + 3 = 7 \\), \\( \\det(A) = 4 \\cdot 3 - 2 \\cdot 1 = 10 \\).<\/p>\n<p>Krok 2 \u2014 r\u00f3wnanie charakterystyczne: \\( \\lambda^2 - 7\\lambda + 10 = 0 \\).<\/p>\n<p>\\[ \\lambda_{1,2} = \\frac{7 \\pm \\sqrt{49 - 40}}{2} = \\frac{7 \\pm 3}{2} \\]<\/p>\n<p>Krok 3 \u2014 warto\u015bci w\u0142asne: \\( \\lambda_1 = 5 \\), \\( \\lambda_2 = 2 \\).<\/p>\n<p>Krok 4 \u2014 wektory w\u0142asne z uk\u0142adu \\( (A - \\lambda I)\\vec{v} = \\vec{0} \\). Dla \\( \\lambda_1 = 5 \\): \\( (4-5)x_1 + 2x_2 = 0 \\), wi\u0119c \\( x_2 = 0{,}5x_1 \\) oraz \\( \\vec{v}_1 = (1,\\ 0{,}5) \\). Dla \\( \\lambda_2 = 2 \\): \\( (4-2)x_1 + 2x_2 = 0 \\), wi\u0119c \\( x_2 = -x_1 \\) oraz \\( \\vec{v}_2 = (1,\\ -1) \\).<\/p>\n<p><strong>Wynik:<\/strong> \\( \\lambda_1 = 5 \\) z wektorem w\u0142asnym \\( (1,\\ 0{,}5) \\); \\( \\lambda_2 = 2 \\) z wektorem w\u0142asnym \\( (1,\\ -1) \\). Sprawdzenie: \\( A\\vec{v}_1 = (5,\\ 2{,}5) = 5\\vec{v}_1 \\) oraz \\( A\\vec{v}_2 = (2,\\ -2) = 2\\vec{v}_2 \\).<\/p>\n<p>\n\r\n<\/section>\n<h2>Jak korzysta\u0107 z kalkulatora warto\u015bci w\u0142asnych<\/h2>\n<ol>\n<li>Wprowad\u017a element <strong>a\u2081\u2081<\/strong> (wiersz 1, kolumna 1). Warto\u015b\u0107 domy\u015blna to 4.<\/li>\n<li>Wprowad\u017a <strong>a\u2081\u2082<\/strong> (wiersz 1, kolumna 2). Warto\u015b\u0107 domy\u015blna to 2.<\/li>\n<li>Wprowad\u017a <strong>a\u2082\u2081<\/strong> (wiersz 2, kolumna 1). Warto\u015b\u0107 domy\u015blna to 1.<\/li>\n<li>Wprowad\u017a <strong>a\u2082\u2082<\/strong> (wiersz 2, kolumna 2). Warto\u015b\u0107 domy\u015blna to 3.<\/li>\n<li>Odczytaj wyniki: wyznacznik |A|, \u015blad, macierz \\( A - cI \\), wielomian charakterystyczny, obie warto\u015bci w\u0142asne oraz wektor w\u0142asny dla ka\u017cdej warto\u015bci w\u0142asnej.<\/li>\n<\/ol>\n<h2>Czym s\u0105 warto\u015bci w\u0142asne i wektory w\u0142asne?<\/h2>\n<p>Wektorem w\u0142asnym macierzy \\( A \\) nazywamy niezerowy wektor, kt\u00f3ry nie zmienia kierunku pod dzia\u0142aniem macierzy \u2014 jest jedynie rozci\u0105gany lub \u015bciskany. Wsp\u00f3\u0142czynnik tego rozci\u0105gania to warto\u015b\u0107 w\u0142asna \\( \\lambda \\). Formalnie, \\( \\vec{v} \\) jest wektorem w\u0142asnym, je\u015bli spe\u0142nia r\u00f3wnanie<\/p>\n<p>\\[ A\\vec{v} = \\lambda\\vec{v} \\]<\/p>\n<p>Geometrycznie macierz 2\u00d72 przekszta\u0142ca p\u0142aszczyzn\u0119: obraca, rozci\u0105ga i \u015bcina wektory. Wi\u0119kszo\u015b\u0107 wektor\u00f3w po przekszta\u0142ceniu wskazuje nowy kierunek, ale co najwy\u017cej dwa szczeg\u00f3lne kierunki przetrwaj\u0105 transformacj\u0119 bez zmiany (poza przeskalowaniem). Te kierunki to wektory w\u0142asne, a ich wsp\u00f3\u0142czynniki skalowania to warto\u015bci w\u0142asne. Dlatego rozk\u0142ad na warto\u015bci w\u0142asne ods\u0142ania \u201eistotne<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Wprowad\u017a cztery elementy macierzy 2\u00d72, aby otrzyma\u0107 jej warto\u015bci w\u0142asne i wektory w\u0142asne, a tak\u017ce wyznacznik, \u015blad i wielomian charakterystyczny wraz z pe\u0142nym rozwi\u0105zaniem krok po kroku.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[6],"tags":[51],"class_list":["post-317","post","type-post","status-publish","format-standard","hentry","category-matematyka","tag-macierze"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/posts\/317","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/comments?post=317"}],"version-history":[{"count":1,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/posts\/317\/revisions"}],"predecessor-version":[{"id":2195,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/posts\/317\/revisions\/2195"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/media?parent=317"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/categories?post=317"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/tags?post=317"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}