{"id":52,"date":"2026-10-03T11:15:33","date_gmt":"2026-10-03T10:15:33","guid":{"rendered":"https:\/\/wpcalc.com\/tr\/matris-toplama\/"},"modified":"2026-10-03T11:15:33","modified_gmt":"2026-10-03T10:15:33","slug":"matris-toplama","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/tr\/matematik\/matris-toplama\/","title":{"rendered":"\u0130ki Matrisin Toplanmas\u0131 Hesaplay\u0131c\u0131s\u0131"},"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\">Matris Toplama \u00c7\u00f6z\u00fcc\u00fcs\u00fc<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"52\" data-favorite-title=\"\u0130ki Matrisin Toplanmas\u0131\" data-favorite-url=\"https:\/\/wpcalc.com\/tr\/matematik\/matris-toplama\/\" data-favorite-excerpt=\"Boyutlar\u0131 ayn\u0131 (2\u00d72 veya 3\u00d73) iki matrisi elemanlar\u0131n\u0131 girerek toplay\u0131n. Hesaplay\u0131c\u0131 kar\u015f\u0131l\u0131kl\u0131 elemanlar\u0131 toplar ve sonu\u00e7 matrisini an\u0131nda g\u00f6r\u00fcnt\u00fcler.\" aria-label=\"Favorilere ekle\" 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\/tr\/matematik\/matris-toplama\/\" method=\"POST\" class=\"calculator\" id=\"calculator-52\" data-post=\"52\"><fieldset class=\"fieldset-input\"><legend class=\"sr-only\">Giri\u015f alanlar\u0131<\/legend><div class=\"field is-single\" id=\"input-1\"><label for=\"field-1\">Matris boyutu<\/label><div class=\"grid grid-cols-1\"><select id=\"field-1\" name=\"matris_boyutu\"><option value=\"2\">2 \u00d7 2<\/option><option value=\"3\">3 \u00d7 3<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><div class=\"is-single field\" id=\"input-2\"><span class=\"font-semibold\">A Matrisi<\/span><\/div><div class=\"field\" id=\"input-3\"><label for=\"field-3\">a\u2081\u2081<\/label><input type=\"number\" name=\"a\" id=\"field-3\" step=\"any\" value=\"1\"\/><\/div><div class=\"field\" id=\"input-4\"><label for=\"field-4\">a\u2081\u2082<\/label><input type=\"number\" name=\"a\" id=\"field-4\" step=\"any\" value=\"2\"\/><\/div><div class=\"field\" id=\"input-5\" hidden><label for=\"field-5\">a\u2081\u2083<\/label><input type=\"number\" name=\"a\" id=\"field-5\" step=\"any\" value=\"3\"\/><\/div><div class=\"field\" id=\"input-6\"><label for=\"field-6\">a\u2082\u2081<\/label><input type=\"number\" name=\"a\" id=\"field-6\" step=\"any\" value=\"4\"\/><\/div><div class=\"field\" id=\"input-7\"><label for=\"field-7\">a\u2082\u2082<\/label><input type=\"number\" name=\"a\" id=\"field-7\" step=\"any\" value=\"5\"\/><\/div><div class=\"field\" id=\"input-8\" hidden><label for=\"field-8\">a\u2082\u2083<\/label><input type=\"number\" name=\"a\" id=\"field-8\" step=\"any\" value=\"6\"\/><\/div><div class=\"field\" id=\"input-9\" hidden><label for=\"field-9\">a\u2083\u2081<\/label><input type=\"number\" name=\"a\" id=\"field-9\" step=\"any\" value=\"7\"\/><\/div><div class=\"field\" id=\"input-10\" hidden><label for=\"field-10\">a\u2083\u2082<\/label><input type=\"number\" name=\"a\" id=\"field-10\" step=\"any\" value=\"8\"\/><\/div><div class=\"field\" id=\"input-11\" hidden><label for=\"field-11\">a\u2083\u2083<\/label><input type=\"number\" name=\"a\" id=\"field-11\" step=\"any\" value=\"9\"\/><\/div><div class=\"is-single field\" id=\"input-12\"><span class=\"font-semibold\">B Matrisi<\/span><\/div><div class=\"field\" id=\"input-13\"><label for=\"field-13\">b\u2081\u2081<\/label><input type=\"number\" name=\"b\" id=\"field-13\" step=\"any\" value=\"1\"\/><\/div><div class=\"field\" id=\"input-14\"><label for=\"field-14\">b\u2081\u2082<\/label><input type=\"number\" name=\"b\" id=\"field-14\" step=\"any\" value=\"0\"\/><\/div><div class=\"field\" id=\"input-15\" hidden><label for=\"field-15\">b\u2081\u2083<\/label><input type=\"number\" name=\"b\" id=\"field-15\" step=\"any\" value=\"0\"\/><\/div><div class=\"field\" id=\"input-16\"><label for=\"field-16\">b\u2082\u2081<\/label><input type=\"number\" name=\"b\" id=\"field-16\" step=\"any\" value=\"0\"\/><\/div><div class=\"field\" id=\"input-17\"><label for=\"field-17\">b\u2082\u2082<\/label><input type=\"number\" name=\"b\" id=\"field-17\" step=\"any\" value=\"1\"\/><\/div><div class=\"field\" id=\"input-18\" hidden><label for=\"field-18\">b\u2082\u2083<\/label><input type=\"number\" name=\"b\" id=\"field-18\" step=\"any\" value=\"0\"\/><\/div><div class=\"field\" id=\"input-19\" hidden><label for=\"field-19\">b\u2083\u2081<\/label><input type=\"number\" name=\"b\" id=\"field-19\" step=\"any\" value=\"0\"\/><\/div><div class=\"field\" id=\"input-20\" hidden><label for=\"field-20\">b\u2083\u2082<\/label><input type=\"number\" name=\"b\" id=\"field-20\" step=\"any\" value=\"0\"\/><\/div><div class=\"field\" id=\"input-21\" hidden><label for=\"field-21\">b\u2083\u2083<\/label><input type=\"number\" name=\"b\" id=\"field-21\" step=\"any\" value=\"1\"\/><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Yeniden hesapla\" id=\"calculate-button\" data-post=\"52\">Hesapla<\/button><button type=\"reset\">S\u0131f\u0131rla<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Otomatik hesapla<\/label><small>Etkinle\u015ftirilirse, herhangi bir de\u011feri de\u011fi\u015ftirdi\u011finizde sonu\u00e7 otomatik olarak g\u00fcncellenir.<\/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> Sonu\u00e7lar\u0131n\u0131z<\/h3><div class=\"result-box\"><div class=\"field-result is-column\" id=\"output-1\"><span class=\"field-title\"><span>Sonu\u00e7<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><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\">Bu hesaplaman\u0131n ba\u011flant\u0131s\u0131n\u0131 kopyala<\/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>Yorum b\u0131rak<\/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=\"52\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">Bu sonu\u00e7 hakk\u0131nda ne d\u00fc\u015f\u00fcn\u00fcyorsunuz?<\/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\">Be\u011fendim <\/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\">Faydal\u0131 <\/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\">Kafam kar\u0131\u015ft\u0131 <\/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\">Hayal k\u0131r\u0131kl\u0131\u011f\u0131 <\/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\">Hatal\u0131 <\/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>Matris Toplama Form\u00fcl\u00fc<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Form\u00fcl<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n\\[ C = A + B = \\begin{bmatrix} a_{11} + b_{11} &amp; a_{12} + b_{12} &amp; \\cdots &amp; a_{1n} + b_{1n} \\\\ a_{21} + b_{21} &amp; a_{22} + b_{22} &amp; \\cdots &amp; a_{2n} + b_{2n} \\\\ \\vdots &amp; \\vdots &amp; \\ddots &amp; \\vdots \\\\ a_{m1} + b_{m1} &amp; a_{m2} + b_{m2} &amp; \\cdots &amp; a_{mn} + b_{mn} \\end{bmatrix} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Burada:<\/strong><\/p>\n<ul>\n<li>\\(A\\) ve \\(B\\) \u2014 boyutlar\u0131 ayn\u0131 \\(m \\times n\\) matrisleri<\/li>\n<li>\\(C\\) \u2014 ayn\u0131 \\(m \\times n\\) boyutunda sonu\u00e7 matrisi<\/li>\n<li>\\(a_{ij}\\), \\(b_{ij}\\) \u2014 \\(A\\) ve \\(B\\) matrislerinin \\(i\\). sat\u0131r, \\(j\\). s\u00fctunundaki elemanlar<\/li>\n<\/ul>\n<p>Sonucun her eleman\u0131, iki matrisin kar\u015f\u0131l\u0131kl\u0131 elemanlar\u0131n\u0131n toplam\u0131d\u0131r: \\(c_{ij} = a_{ij} + b_{ij}\\).<\/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>\u0130ki Matrisin Toplanmas\u0131 \u2013 Hesaplama \u00d6rne\u011fi<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>\u00d6rnek:<\/strong> hesaplay\u0131c\u0131n\u0131n varsay\u0131lan de\u011ferlerini kullanarak 3\u00d73 bir \\(A\\) matrisini birim matris \\(B\\) ile toplay\u0131n.<\/p>\n<p>\\[ A = \\begin{bmatrix} 1 &amp; 2 &amp; 3 \\\\ 4 &amp; 5 &amp; 6 \\\\ 7 &amp; 8 &amp; 9 \\end{bmatrix}, \\quad B = \\begin{bmatrix} 1 &amp; 0 &amp; 0 \\\\ 0 &amp; 1 &amp; 0 \\\\ 0 &amp; 0 &amp; 1 \\end{bmatrix} \\]<\/p>\n<p>\\[ C = A + B = \\begin{bmatrix} 1+1 &amp; 2+0 &amp; 3+0 \\\\ 4+0 &amp; 5+1 &amp; 6+0 \\\\ 7+0 &amp; 8+0 &amp; 9+1 \\end{bmatrix} = \\begin{bmatrix} 2 &amp; 2 &amp; 3 \\\\ 4 &amp; 6 &amp; 6 \\\\ 7 &amp; 8 &amp; 10 \\end{bmatrix} \\]<\/p>\n<p><strong>Sonu\u00e7:<\/strong> iki matrisin toplam\u0131 \\(C = \\begin{bmatrix} 2 &amp; 2 &amp; 3 \\\\ 4 &amp; 6 &amp; 6 \\\\ 7 &amp; 8 &amp; 10 \\end{bmatrix}\\) olur. Birim matrisin eklenmesinin, \\(A\\) matrisinin k\u00f6\u015fegen elemanlar\u0131 hari\u00e7 (bunlar\u0131n her biri 1 artar) t\u00fcm elemanlar\u0131n\u0131 nas\u0131l de\u011fi\u015ftirmedi\u011fine dikkat edin.<\/p>\n<p>\n\r\n<\/section>\n<h2>Hesaplay\u0131c\u0131 nas\u0131l kullan\u0131l\u0131r<\/h2>\n<ol>\n<li>\u00dcstteki a\u00e7\u0131l\u0131r listeden <strong>Matris boyutunu<\/strong> se\u00e7in \u2014 2 \u00d7 2 ya da 3 \u00d7 3. Her iki matris de ayn\u0131 boyutta olmal\u0131d\u0131r.<\/li>\n<li>\\(a_{11}, a_{12}, \\ldots\\) alanlar\u0131na <strong>A Matrisinin<\/strong> elemanlar\u0131n\u0131 girin. Her alt simge, eleman\u0131n hangi sat\u0131r ve s\u00fctunda oldu\u011funu g\u00f6sterir (\u00f6rne\u011fin \\(a_{21}\\), 2. sat\u0131r 1. s\u00fctundur).<\/li>\n<li><strong>B Matrisinin<\/strong> elemanlar\u0131n\u0131 da ayn\u0131 \u015fekilde \\(b_{11}, b_{12}, \\ldots\\) alanlar\u0131na girin.<\/li>\n<li>Sonu\u00e7 hemen g\u00f6r\u00fcn\u00fcr: kar\u015f\u0131l\u0131kl\u0131 elemanlar\u0131n toplamlar\u0131ndan olu\u015fan \\(C = A + B\\) matrisini g\u00f6steren bir tablo. De\u011ferler iki ondal\u0131k basama\u011fa yuvarlan\u0131r.<\/li>\n<\/ol>\n<h2>Matris toplama nedir?<\/h2>\n<p>Matris toplama, do\u011frusal cebirdeki en basit i\u015flemlerden biridir. \u0130ki matrisi toplamak i\u00e7in kar\u015f\u0131l\u0131kl\u0131 elemanlar\u0131 toplars\u0131n\u0131z \u2014 sonucun \\(i\\). sat\u0131r, \\(j\\). s\u00fctunundaki eleman, iki orijinal matrisin ayn\u0131 konumlar\u0131ndaki elemanlar\u0131n toplam\u0131na e\u015fittir. \u0130\u015flem yaln\u0131zca boyutlar\u0131 birebir ayn\u0131 olan matrisler i\u00e7in tan\u0131ml\u0131d\u0131r: 2\u00d72 bir matris 2\u00d72 bir matrisle toplanabilir, ancak 3\u00d73 bir matrisle toplanamaz; \u00e7\u00fcnk\u00fc toplenecek kar\u015f\u0131l\u0131\u011f\u0131 olmayan elemanlar ortaya \u00e7\u0131kard\u0131.<\/p>\n<p>S\u0131raya ba\u011fl\u0131 ve \u00e7ok daha karma\u015f\u0131k olan matris \u00e7arp\u0131m\u0131n\u0131n aksine, toplama eleman eleman yap\u0131l\u0131r ve s\u0131radan say\u0131 toplam\u0131na \u00e7ok benzer. Bu, onu matris i\u015flemlerini \u00f6\u011frenirken do\u011fal bir ba\u015flang\u0131\u00e7 noktas\u0131 yapar; ayr\u0131ca uygulamal\u0131 \u00e7al\u0131\u015fmalarda s\u00fcrekli kullan\u0131l\u0131r: fizik ve m\u00fchendislikte kuvvetlerin veya yer de\u011fi\u015ftirmelerin toplanmas\u0131, g\u00f6r\u00fcnt\u00fc i\u015flemede piksel verilerinin birle\u015ftirilmesi, makine \u00f6\u011frenmesinde a\u011f\u0131rl\u0131klar\u0131n toplanmas\u0131 ve ekonomi ile istatistikte de\u011fer tablolar\u0131n\u0131n birle\u015ftirilmesi.<\/p>\n<p>Sonucun yorumlanmas\u0131 olduk\u00e7a basittir: \\(C\\) matrisinin her eleman\u0131, \\(A\\) ve \\(B\\) matrislerinin kar\u015f\u0131l\u0131kl\u0131 elemanlar\u0131n\u0131n birle\u015fik etkisini tan\u0131mlar. \u00d6rne\u011fin, iki matris iki farkl\u0131 ma\u011fazadaki \u00e7e\u015fitli \u00fcr\u00fcnlerin ayl\u0131k sat\u0131\u015flar\u0131n\u0131 tutuyorsa, toplamlar\u0131 her iki ma\u011fazadaki birle\u015fik sat\u0131\u015flar\u0131 verir. Yukar\u0131daki \u00f6rnekteki gibi birim matrisin eklenmesi, k\u00f6\u015fegen d\u0131\u015f\u0131 t\u00fcm elemanlar\u0131 de\u011fi\u015ftirmez ve her k\u00f6\u015fegen eleman\u0131 1 art\u0131r\u0131r.<\/p>\n<h2>Matris toplaman\u0131n \u00f6zellikleri<\/h2>\n<p>Matris toplama, ger\u00e7ek say\u0131lar\u0131n toplanmas\u0131yla ayn\u0131 bilinen kurallara uyar:<\/p>\n<ul>\n<li><strong>De\u011fi\u015fme \u00f6zelli\u011fi:<\/strong> \\(A + B = B + A\\) \u2014 matrislerin s\u0131ras\u0131 \u00f6nemli de\u011fildir.<\/li>\n<li><strong>Birle\u015fme \u00f6zelli\u011fi:<\/strong> \\((A + B) + C = A + (B + C)\\) \u2014 grupland\u0131rma sonucu etkilemez.<\/li>\n<li><strong>Birim eleman:<\/strong> \\(A + O = A\\); burada \\(O\\), ayn\u0131 boyutta s\u0131f\u0131r matrisidir.<\/li>\n<li><strong>Ters eleman:<\/strong> \\(A + (-A) = O\\); burada \\(-A\\), \\(A\\) matrisinin t\u00fcm elemanlar\u0131n\u0131n i\u015fareti ters \u00e7evrilmi\u015f matristir.<\/li>\n<\/ul>\n<p>Bu \u00f6zelliklerin toplama i\u00e7in ge\u00e7erli oldu\u011funu, \u00e7arpmaya de\u011fil, unutmay\u0131n: genel olarak \\(AB \\neq BA\\) olur ve \\(A + B\\)'nin \u00e7arp\u0131mda do\u011frudan bir kar\u015f\u0131l\u0131\u011f\u0131 yoktur. \u0130ki matrisin \u00e7arp\u0131m\u0131na ihtiyac\u0131n\u0131z varsa <a href=\"https:\/\/wpcalc.com\/tr\/matematik\/matris-carpimi\/\">Matris \u00c7arp\u0131m\u0131<\/a> hesaplay\u0131c\u0131s\u0131n\u0131 kullan\u0131n; iki matrisin fark\u0131 i\u00e7in <a href=\"https:\/\/wpcalc.com\/tr\/matematik\/matris-cikarma\/\">\u0130ki Matrisin \u00c7\u0131kar\u0131lmas\u0131<\/a> hesaplay\u0131c\u0131s\u0131na bak\u0131n.<\/p>\n<h2>Varsay\u0131mlar ve s\u0131n\u0131rlamalar<\/h2>\n<ul>\n<li><strong>E\u015fit boyut zorunlulu\u011fu.<\/strong> Hesaplay\u0131c\u0131 yaln\u0131zca ayn\u0131 boyuttaki matrisleri toplar. Farkl\u0131 boyutlardaki matrisler tan\u0131m gere\u011fi toplanamaz.<\/li>\n<li><strong>Desteklenen boyutlar.<\/strong> Yaln\u0131zca 2 \u00d7 2 ve 3 \u00d7 3 matrisler desteklenir. Daha b\u00fcy\u00fck matrisler i\u00e7in de ayn\u0131 eleman eleman kural\u0131 ge\u00e7erlidir, ancak daha genel bir araca ihtiya\u00e7 duyars\u0131n\u0131z.<\/li>\n<li><strong>Say\u0131sal giri\u015fler.<\/strong> T\u00fcm elemanlar say\u0131 (tam say\u0131 veya ondal\u0131kl\u0131) olmal\u0131d\u0131r. Kesirli de\u011ferlerin girmeden \u00f6nce ondal\u0131k forma d\u00f6n\u00fc\u015ft\u00fcr\u00fclmesi gerekir.<\/li>\n<li><strong>Yuvarlama.<\/strong> Sonu\u00e7lar iki ondal\u0131k basama\u011fa yuvarlanarak g\u00f6r\u00fcnt\u00fclenir; bu, \u00e7o\u011fu ders \u00e7al\u0131\u015fmas\u0131 ve pratik uygulama i\u00e7in yeterlidir.<\/li>\n<li><strong>Determinantlar toplanmaz.<\/strong> Genel olarak \\(\\det(A + B) \\neq \\det(A) + \\det(B)\\). Sonu\u00e7 matrisinin determinant\u0131na ihtiyac\u0131n\u0131z varsa ya da <a href=\"https:\/\/wpcalc.com\/tr\/matematik\/determinant-toplami\/\">Determinantlar\u0131n Toplam\u0131<\/a> ile kar\u015f\u0131la\u015ft\u0131rmak istiyorsan\u0131z, determinant\u0131 ayr\u0131 matrislerden de\u011fil, son matristen hesaplay\u0131n.<\/li>\n<\/ul>\n<h2>Pratik ipu\u00e7lar\u0131<\/h2>\n<ul>\n<li>Elemanlar\u0131 do\u011fru konumlara girdi\u011finizi iki kez kontrol edin \u2014 \u00f6nce sat\u0131r, sonra s\u00fctun. S\u0131k yap\u0131lan bir hata, bir eleman\u0131 devri\u015f (transpose) yapmakt\u0131r; \u00f6rne\u011fin \\(a_{21}\\) de\u011ferini \\(a_{12}\\) alan\u0131na girmek.<\/li>\n<li>Elde hesaplar\u0131n\u0131z\u0131 do\u011frulamak i\u00e7in sonucu kullan\u0131n: bir veya iki eleman\u0131 kendiniz hesaplay\u0131n ve hesaplay\u0131c\u0131n\u0131n \u00e7\u0131kt\u0131s\u0131yla kar\u015f\u0131la\u015ft\u0131r\u0131n.<\/li>\n<li>\u0130lgili i\u015flemler i\u00e7in, sonu\u00e7 matrisini daha ileri analiz ederken <a href=\"https:\/\/wpcalc.com\/tr\/matematik\/3x3-matris-tersi\/\">3\u00d73 Matrisin Tersi<\/a> ve <a href=\"https:\/\/wpcalc.com\/tr\/matematik\/3x3-matris-rank-hesaplama\/\">3\u00d73 Matrisin Rank\u0131<\/a> hesaplay\u0131c\u0131lar\u0131 da i\u015finize yarayabilir.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Boyutlar\u0131 ayn\u0131 (2\u00d72 veya 3\u00d73) iki matrisi elemanlar\u0131n\u0131 girerek toplay\u0131n. Hesaplay\u0131c\u0131 kar\u015f\u0131l\u0131kl\u0131 elemanlar\u0131 toplar ve sonu\u00e7 matrisini an\u0131nda g\u00f6r\u00fcnt\u00fcler.<\/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":[8],"tags":[54],"class_list":["post-52","post","type-post","status-publish","format-standard","hentry","category-matematik","tag-matris"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/52","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/comments?post=52"}],"version-history":[{"count":5,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/52\/revisions"}],"predecessor-version":[{"id":3657,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/52\/revisions\/3657"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/media?parent=52"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/categories?post=52"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/tags?post=52"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}