{"id":64880,"date":"2025-06-20T09:43:31","date_gmt":"2025-06-20T06:43:31","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=64880"},"modified":"2025-06-20T09:44:37","modified_gmt":"2025-06-20T06:44:37","slug":"matrix-addition","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/mathematics\/matrix-addition\/","title":{"rendered":"Addition of Two Matrices Calculator"},"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 class=\"text-lg font-display font-bold\">Matrix Addition Solver<\/h2><\/div><div class=\"relative group inline-block\">\n  <button class=\"favorite\" id=\"favorite\" data-favorite-id=\"64880\" data-favorite-title=\"Addition of Two Matrices\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/mathematics\/matrix-addition\/\" data-favorite-excerpt=\"This calculator helps you add two matrices of the same dimensions by summing their corresponding elements. 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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\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">Like <\/span><\/button><button 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\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">Helpful <\/span><\/button><button 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\">\ud83d\ude15 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backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><ins class=\"adsbygoogle\"\n     style=\"display:block; text-align:center; margin: 32px 0;\"\n     data-ad-layout=\"in-article\"\n     data-ad-format=\"fluid\"\n     data-ad-client=\"ca-pub-1721569815777345\"\n     data-ad-slot=\"6317458308\"><\/ins>\n<script>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script>\n<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>Matrix Addition Formula<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Formula<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n$$C = A + B =\n\\begin{bmatrix}\na_{11} + b_{11} &#038; a_{12} + b_{12} &#038; \\cdots &#038; a_{1n} + b_{1n} \\\\\na_{21} + b_{21} &#038; a_{22} + b_{22} &#038; \\cdots &#038; a_{2n} + b_{2n} \\\\\n\\vdots &#038; \\vdots &#038; \\ddots &#038; \\vdots \\\\\na_{m1} + b_{m1} &#038; a_{m2} + b_{m2} &#038; \\cdots &#038; a_{mn} + b_{mn}\n\\end{bmatrix}\n$$\n<\/div>\r\n\t<\/figure>\r\n\t<br \/>\nWhere:<\/p>\n<ul>\n<li>$$A$$ and $$B$$ are matrices of size $$m \\times n$$<\/li>\n<li>$$C$$ is the resulting matrix after addition<\/li>\n<\/ul>\n<p>Each element of $$C$$ is obtained by adding the corresponding elements of matrices $$A$$ and $$B$$.<br \/>\r\n<\/section>\n<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>Addition of Two Matrices \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p>$$A = \\begin{bmatrix} 1 &#038; 2 \\\\ 3 &#038; 4 \\end{bmatrix}, \\quad B = \\begin{bmatrix} 5 &#038; 6 \\\\ 7 &#038; 8 \\end{bmatrix}$$<\/p>\n<p>$$C = A + B = \\begin{bmatrix} 1 + 5 &#038; 2 + 6 \\\\ 3 + 7 &#038; 4 + 8 \\end{bmatrix} = \\begin{bmatrix} 6 &#038; 8 \\\\ 10 &#038; 12\\end{bmatrix}$$<\/p>\n\r\n<\/section>\n<p>Matrix addition is a fundamental operation in linear algebra, used in systems of equations, computer graphics, and data processing. It requires both matrices to have identical dimensions. Our calculator automates this process, making matrix addition fast and error-free.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This calculator helps you add two matrices of the same dimensions by summing their corresponding elements. It\u2019s perfect for students, engineers, and scientists working with linear algebra and matrix operations.<\/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":[7],"tags":[69],"class_list":["post-64880","post","type-post","status-publish","format-standard","hentry","category-mathematics","tag-matrix"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/64880","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/comments?post=64880"}],"version-history":[{"count":3,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/64880\/revisions"}],"predecessor-version":[{"id":64883,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/64880\/revisions\/64883"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=64880"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=64880"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=64880"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}