{"id":4014,"date":"2026-10-14T23:24:31","date_gmt":"2026-10-14T22:24:31","guid":{"rendered":"https:\/\/wpcalc.com\/tr\/matematik\/matris-skaler-carpim-hesaplama\/"},"modified":"2026-10-14T23:24:31","modified_gmt":"2026-10-14T22:24:31","slug":"matris-skaler-carpim-hesaplama","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/tr\/matematik\/matris-skaler-carpim-hesaplama\/","title":{"rendered":"Matris Skaler \u00c7arp\u0131m\u0131 Hesaplama Arac\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\">Bir matrisi skalerle (sabit say\u0131yla) \u00e7arpma<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"4014\" data-favorite-title=\"Matris Skaler \u00c7arp\u0131m\u0131\" data-favorite-url=\"https:\/\/wpcalc.com\/tr\/matematik\/matris-skaler-carpim-hesaplama\/\" data-favorite-excerpt=\"2 \u00d7 2 veya 3 \u00d7 3 bir matrisi bir skalerle (sabit say\u0131yla) \u00e7arp\u0131n. Skaler k&#039;yi ve A matrisinin elemanlar\u0131n\u0131 girin; kA matrisi an\u0131nda kar\u015f\u0131n\u0131za \u00e7\u0131ks\u0131n.\" 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-skaler-carpim-hesaplama\/\" method=\"POST\" class=\"calculator\" id=\"calculator-4014\" data-post=\"4014\"><fieldset class=\"fieldset-input is-3\"><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\" selected>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=\"field is-single has-term\" id=\"input-2\"><label for=\"field-2\">Skaler (k)<\/label><div class=\"term\">k<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"skaler_k\" id=\"field-2\" aria-describedby=\"calc-info-2\" step=\"any\" value=\"3\"\/><small id=\"calc-info-2\">T\u00fcm elemanlar\u0131n \u00e7arp\u0131laca\u011f\u0131 sabit say\u0131<\/small><\/div><div class=\"is-single field\" id=\"input-3\"><span class=\"font-semibold\">A matrisi<\/span><\/div><div class=\"field\" id=\"input-4\"><label for=\"field-4\">a\u2081\u2081<\/label><input type=\"number\" name=\"a\" id=\"field-4\" step=\"any\" value=\"1\"\/><\/div><div class=\"field\" id=\"input-5\"><label for=\"field-5\">a\u2081\u2082<\/label><input type=\"number\" name=\"a\" id=\"field-5\" step=\"any\" value=\"2\"\/><\/div><div class=\"field\" id=\"input-6\" hidden><label for=\"field-6\">a\u2081\u2083<\/label><input type=\"number\" name=\"a\" id=\"field-6\" step=\"any\" value=\"3\"\/><\/div><div class=\"field\" id=\"input-7\"><label for=\"field-7\">a\u2082\u2081<\/label><input type=\"number\" name=\"a\" id=\"field-7\" step=\"any\" value=\"4\"\/><\/div><div class=\"field\" id=\"input-8\"><label for=\"field-8\">a\u2082\u2082<\/label><input type=\"number\" name=\"a\" id=\"field-8\" step=\"any\" value=\"5\"\/><\/div><div class=\"field\" id=\"input-9\" hidden><label for=\"field-9\">a\u2082\u2083<\/label><input type=\"number\" name=\"a\" id=\"field-9\" step=\"any\" value=\"6\"\/><\/div><div class=\"field\" id=\"input-10\" hidden><label for=\"field-10\">a\u2083\u2081<\/label><input type=\"number\" name=\"a\" id=\"field-10\" step=\"any\" value=\"7\"\/><\/div><div class=\"field\" id=\"input-11\" hidden><label for=\"field-11\">a\u2083\u2082<\/label><input type=\"number\" name=\"a\" id=\"field-11\" step=\"any\" value=\"8\"\/><\/div><div class=\"field\" id=\"input-12\" hidden><label for=\"field-12\">a\u2083\u2083<\/label><input type=\"number\" name=\"a\" id=\"field-12\" step=\"any\" value=\"9\"\/><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Yeniden hesapla\" id=\"calculate-button\" data-post=\"4014\">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 matrisi (kA)<\/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=\"4014\" 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>Matrisin Skalerle \u00c7arp\u0131m\u0131 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\\[ kA = k \\begin{bmatrix} a_{11} &amp; a_{12} &amp; \\cdots &amp; a_{1n} \\\\ a_{21} &amp; a_{22} &amp; \\cdots &amp; a_{2n} \\\\ \\vdots &amp; \\vdots &amp; \\ddots &amp; \\vdots \\\\ a_{n1} &amp; a_{n2} &amp; \\cdots &amp; a_{nn} \\end{bmatrix} = \\begin{bmatrix} k\\,a_{11} &amp; k\\,a_{12} &amp; \\cdots &amp; k\\,a_{1n} \\\\ k\\,a_{21} &amp; k\\,a_{22} &amp; \\cdots &amp; k\\,a_{2n} \\\\ \\vdots &amp; \\vdots &amp; \\ddots &amp; \\vdots \\\\ k\\,a_{n1} &amp; k\\,a_{n2} &amp; \\cdots &amp; k\\,a_{nn} \\end{bmatrix} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Burada:<\/strong><\/p>\n<ul>\n<li>\\(k\\) \u2014 skaler (herhangi bir ger\u00e7ek sabit)<\/li>\n<li>\\(A\\) \u2014 \u00f6zg\u00fcn \\(n \\times n\\) matris<\/li>\n<li>\\(a_{ij}\\) \u2014 \\(A\\) matrisinin \\(i\\). sat\u0131r ve \\(j\\). s\u00fctunundaki eleman<\/li>\n<li>\\(kA\\) \u2014 sonu\u00e7 matrisi; buradaki her eleman, \\(A\\)'n\u0131n ilgili eleman\u0131n\u0131n \\(k\\) kat\u0131d\u0131r<\/li>\n<\/ul>\n<p>Skalerle \u00e7arpma, matrisin her eleman\u0131n\u0131 ayn\u0131 sabitle \u00f6l\u00e7ekler. Matrisin boyutu ve bi\u00e7imi asla de\u011fi\u015fmez \u2014 yaln\u0131zca de\u011ferler de\u011fi\u015fir.<\/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>Matrisin Skalerle \u00c7arp\u0131m\u0131 \u2013 \u00d6rnek Hesaplama<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>\u00d6rnek:<\/strong> a\u015fa\u011f\u0131daki 3 \u00d7 3'l\u00fck \\(A\\) matrisini \\(k = 3\\) skaleriyle \u00e7arp\u0131n.<\/p>\n<p>\\[ A = \\begin{bmatrix} 1 &amp; 2 &amp; 3 \\\\ 4 &amp; 5 &amp; 6 \\\\ 7 &amp; 8 &amp; 9 \\end{bmatrix} \\]<\/p>\n<p>Her eleman 3 ile \u00e7arp\u0131l\u0131r:<\/p>\n<p>\\[ 3A = \\begin{bmatrix} 3 \\cdot 1 &amp; 3 \\cdot 2 &amp; 3 \\cdot 3 \\\\ 3 \\cdot 4 &amp; 3 \\cdot 5 &amp; 3 \\cdot 6 \\\\ 3 \\cdot 7 &amp; 3 \\cdot 8 &amp; 3 \\cdot 9 \\end{bmatrix} = \\begin{bmatrix} 3 &amp; 6 &amp; 9 \\\\ 12 &amp; 15 &amp; 18 \\\\ 21 &amp; 24 &amp; 27 \\end{bmatrix} \\]<\/p>\n<p><strong>Sonu\u00e7:<\/strong> sonu\u00e7 matrisi \\(\\begin{bmatrix} 3 &amp; 6 &amp; 9 \\\\ 12 &amp; 15 &amp; 18 \\\\ 21 &amp; 24 &amp; 27 \\end{bmatrix}\\)'dir.<\/p>\n<p>\n\r\n<\/section>\n<h2>Hesaplay\u0131c\u0131 nas\u0131l kullan\u0131l\u0131r?<\/h2>\n<ol>\n<li>A\u00e7\u0131l\u0131r listeden <strong>Matris boyutunu<\/strong> se\u00e7in \u2014 2 \u00d7 2 ya da 3 \u00d7 3. 2 \u00d7 2'yi se\u00e7ti\u011finizde \u00fc\u00e7\u00fcnc\u00fc sat\u0131r ve s\u00fctun alanlar\u0131 otomatik olarak gizlenir.<\/li>\n<li><strong>Skaler (k)<\/strong> alan\u0131na sabiti girin. Bu say\u0131 pozitif, negatif, s\u0131f\u0131r ya da ondal\u0131kl\u0131 olabilir.<\/li>\n<li><strong>A matrisinin<\/strong> g\u00f6r\u00fcn\u00fcr durumdaki t\u00fcm elemanlar\u0131n\u0131 doldurun (a\u2081\u2081, a\u2081\u2082, a\u2081\u2083, a\u2082\u2081 vb.). Alt simge konumu g\u00f6sterir: ilk say\u0131 sat\u0131r\u0131, ikinci say\u0131 s\u00fctunu belirtir.<\/li>\n<li>\u201cSonu\u00e7lar\u0131n\u0131z\u201d alt\u0131nda g\u00f6r\u00fcnen <strong>Sonu\u00e7 Matrisini (kA)<\/strong> okuyun. Her h\u00fccre, \\(A\\)'n\u0131n ilgili eleman\u0131n\u0131n \\(k\\) ile \u00e7arp\u0131m\u0131n\u0131 iki ondal\u0131k basama\u011fa yuvarlanm\u0131\u015f olarak g\u00f6sterir.<\/li>\n<\/ol>\n<h2>Matrisin skalerle \u00e7arp\u0131m\u0131 nedir?<\/h2>\n<p>Lineer cebirde <strong>skaler<\/strong> tek bir say\u0131d\u0131r; matris ise say\u0131lar\u0131n dikd\u00f6rtgen bir dizilimidir. Bir matrisi bir skalerle \u00e7arpmak, o matrisin <em>t\u00fcm elemanlar\u0131n\u0131<\/em> ayn\u0131 say\u0131yla \u00e7arpmak demektir. Sonu\u00e7, tam olarak ayn\u0131 boyutlarda yeni bir matristir \u2014 skalerle \u00e7arpma asla matrisin boyutunu de\u011fi\u015ftirmez.<\/p>\n<p>Bu i\u015flem, iki matrisin sat\u0131r-s\u00fctun i\u00e7 \u00e7arp\u0131mlar\u0131 yoluyla \u00e7arp\u0131ld\u0131\u011f\u0131 <em>matris \u00e7arp\u0131m\u0131ndan<\/em> farkl\u0131d\u0131r. Skalerle \u00e7arpma \u00e7ok daha basittir: eleman elemana uygulanan s\u0131radan bir \u00e7arpma i\u015fleminden ibarettir. \u00d6rne\u011fin \\(k = 2\\) ise ve \\(A\\)'n\u0131n bir eleman\u0131 5 ise, \\(kA\\)'n\u0131n ilgili eleman\u0131 \\(2 \\times 5 = 10\\)'dur.<\/p>\n<p>Geometrik a\u00e7\u0131dan, bir matris uzay\u0131n bir d\u00f6n\u00fc\u015f\u00fcm\u00fcn\u00fc temsil ediyorsa, onu \\(k\\) skaleriyle \u00e7arpmak bu d\u00f6n\u00fc\u015f\u00fcm\u00fc her y\u00f6nde \\(k\\) kadar gerer (ya da b\u00fczer). \\(k &gt; 1\\) iken sonu\u00e7 b\u00fcy\u00fct\u00fclm\u00fc\u015f olur, \\(0 &lt; k &lt; 1\\) iken k\u00fc\u00e7\u00fclt\u00fclm\u00fc\u015f olur; \\(k\\) negatifken ise sonu\u00e7 orijine g\u00f6re yans\u0131t\u0131l\u0131r: her eleman\u0131n i\u015fareti de\u011fi\u015fir.<\/p>\n<p>Skalerle \u00e7arpma uygulamal\u0131 \u00e7al\u0131\u015fmalarda s\u0131k s\u0131k kar\u015f\u0131n\u0131za \u00e7\u0131kar: denklemler sistemlerinde katsay\u0131 matrislerini \u00f6l\u00e7ekleme (<a href=\"https:\/\/wpcalc.com\/tr\/matematik\/yok-etme-yontemi\/\">eleme y\u00f6ntemi<\/a> ile ili\u015fkili), veri tablolar\u0131n\u0131 normalize etme, a\u011f\u0131rl\u0131klar\u0131 ayarlama ve matrislerin lineer kombinasyonlar\u0131n\u0131 kurma. Ayr\u0131ca skalerle \u00e7arpma matris toplam\u0131yla da uyum i\u00e7indedir: \\(k(A + B) = kA + kB\\).<\/p>\n<h2>Temel \u00f6zellikler<\/h2>\n<ul>\n<li><strong>Sonucun boyutu:<\/strong> \\(kA\\) her zaman \\(A\\) ile ayn\u0131 boyutlardad\u0131r.<\/li>\n<li><strong>Skalerle de\u011fi\u015fmelilik:<\/strong> \\(kA = Ak\\) \u2014 skalerin hangi tarafta yaz\u0131ld\u0131\u011f\u0131 fark etmez.<\/li>\n<li><strong>Birle\u015fme \u00f6zelli\u011fi:<\/strong> \\(c(kA) = (ck)A\\) \u2014 art arda iki skalerle \u00e7arpmak, bir kez \u00e7arp\u0131mlar\u0131yla \u00e7arpmakla ayn\u0131 sonucu verir.<\/li>\n<li><strong>Skalerlere g\u00f6re da\u011f\u0131lma:<\/strong> \\((c + k)A = cA + kA\\).<\/li>\n<li><strong>Matrislere g\u00f6re da\u011f\u0131lma:<\/strong> \\(k(A + B) = kA + kB\\).<\/li>\n<li><strong>1 ile \u00e7arpma:<\/strong> \\(1 \\cdot A = A\\) \u2014 birim skaler matrisi de\u011fi\u015ftirmez.<\/li>\n<li><strong>0 ile \u00e7arpma:<\/strong> \\(0 \\cdot A\\) s\u0131f\u0131r matrisidir \u2014 her eleman 0 olur.<\/li>\n<li><strong>Negatif skalerler:<\/strong> \\((-1)A\\) her eleman\u0131n i\u015faretini tersine \u00e7evirir; bu tam olarak \\(-A\\) matrisidir.<\/li>\n<\/ul>\n<h2>S\u0131n\u0131rlamalar ve pratik ipu\u00e7lar\u0131<\/h2>\n<ul>\n<li>Bu hesaplay\u0131c\u0131 <strong>yaln\u0131zca kare matrislerle<\/strong> (2 \u00d7 2 veya 3 \u00d7 3) \u00e7al\u0131\u015f\u0131r. Dikd\u00f6rtgen matrisler i\u00e7in de ayn\u0131 kural\u0131 elle uygulayabilirsiniz: her eleman\u0131 \\(k\\) ile \u00e7arp\u0131n.<\/li>\n<li>Sonu\u00e7lar g\u00f6r\u00fcnt\u00fclenirken iki ondal\u0131k basama\u011fa yuvarlan\u0131r; bu nedenle \u00e7ok say\u0131da ondal\u0131k basama\u011f\u0131 olan elemanlar hafif\u00e7e yuvarlanm\u0131\u015f g\u00f6r\u00fcnebilir. Tam sonu\u00e7 gerekti\u011finde tam say\u0131 ya da basit kesir de\u011ferleri girin.<\/li>\n<li>\u00c7ok b\u00fcy\u00fck skalerler veya elemanlar b\u00fcy\u00fck sonu\u00e7lar do\u011furabilir; hesaplay\u0131c\u0131 kayan noktal\u0131 say\u0131larla \u00e7al\u0131\u015ft\u0131\u011f\u0131ndan a\u015f\u0131r\u0131 de\u011ferlerde duyarl\u0131l\u0131k kayb\u0131 ya\u015fanabilir.<\/li>\n<li>\\(kA\\) (skalerle \u00e7arpma) ile \\(k \\cdot I\\) (bir skaler \u00e7arp\u0131 birim matris) aras\u0131ndaki fark\u0131 akl\u0131n\u0131zda tutun. Bunlar ayn\u0131 \u015fey de\u011fildir: \\(kI\\)'nin k\u00f6\u015fegeninde \\(k\\), di\u011fer h\u00fccrelerinde s\u0131f\u0131r bulunur.<\/li>\n<li>Bir lineer sistemi \u00e7\u00f6zerken matrisi \u00f6l\u00e7ekliyorsan\u0131z, her sat\u0131r i\u015flemi geni\u015fletilmi\u015f matrisin tamam\u0131na uygulanmal\u0131d\u0131r \u2014 bu i\u015f ak\u0131\u015f\u0131 i\u00e7in <a href=\"https:\/\/wpcalc.com\/tr\/matematik\/yok-etme-yontemi\/\">eleme y\u00f6ntemi hesaplay\u0131c\u0131s\u0131na<\/a> bak\u0131n ya da kare \u0131zgaralardaki desenleri ke\u015ffetmek i\u00e7in <a href=\"https:\/\/wpcalc.com\/tr\/matematik\/sihirli-kare-uretici\/\">b\u00fcy\u00fcl\u00fc kare \u00fcretecini<\/a> deneyin.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>2 \u00d7 2 veya 3 \u00d7 3 bir matrisi bir skalerle (sabit say\u0131yla) \u00e7arp\u0131n. Skaler k'yi ve A matrisinin elemanlar\u0131n\u0131 girin; kA matrisi an\u0131nda kar\u015f\u0131n\u0131za \u00e7\u0131ks\u0131n.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[8],"tags":[54],"class_list":["post-4014","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\/4014","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=4014"}],"version-history":[{"count":0,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/4014\/revisions"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/media?parent=4014"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/categories?post=4014"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/tags?post=4014"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}