{"id":2326,"date":"2022-04-23T04:49:19","date_gmt":"2022-04-23T04:49:19","guid":{"rendered":"https:\/\/swatilathia.com\/?page_id=2326"},"modified":"2022-09-12T10:14:09","modified_gmt":"2022-09-12T10:14:09","slug":"introduction-properties","status":"publish","type":"page","link":"https:\/\/swatilathia.com\/?page_id=2326","title":{"rendered":"Introduction &#038; Properties"},"content":{"rendered":"<body>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<label for=\"ez-toc-cssicon-toggle-item-69f6432c50224\" class=\"ez-toc-cssicon-toggle-label\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/label><input type=\"checkbox\"  id=\"ez-toc-cssicon-toggle-item-69f6432c50224\"  aria-label=\"Toggle\" \/><nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/swatilathia.com\/?page_id=2326\/#Determinant_of_a_Matrix\" >Determinant of a Matrix<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/swatilathia.com\/?page_id=2326\/#Properties_of_Determinants\" >Properties of Determinants<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/swatilathia.com\/?page_id=2326\/#If_the_rows_of_a_determinant_are_changed_into_columns_and_vice_verse_the_value_of_the_determinant_remains_unchanged_ie_A_At\" >If the rows of a determinant are changed into columns and vice verse, the value of the determinant remains unchanged. i.e. |A| = |At|<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/swatilathia.com\/?page_id=2326\/#If_any_two_rows_or_columns_are_interchanged_the_value_of_the_resulting_determinant_is_additive_inverse_of_the_value_of_the_original_determinant_ie_A_-A\" >If any two rows (or columns) are interchanged, the value of the resulting determinant is additive inverse of the value of the original determinant. i.e. |A| = -|A|<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/swatilathia.com\/?page_id=2326\/#If_any_two_rows_or_columns_of_the_determinant_are_identical_the_determinants_value_is_zero\" >If any two rows or columns of the determinant are identical, the determinant\u2019s value is zero.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/swatilathia.com\/?page_id=2326\/#If_the_elements_of_a_row_or_column_of_a_determinant_are_added_subtracted_k-times_the_corresponding_elements_of_another_row_column_the_value_of_the_determinant_so_obtained_remains_unchanged\" >If the elements of a row (or column) of a determinant are added (subtracted) k-times the corresponding elements of another row (column), the value of the determinant so obtained remains unchanged.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/swatilathia.com\/?page_id=2326\/#If_the_elements_of_a_row_column_of_a_matrix_are_multiplied_by_the_same_number_say_k_the_determinant_of_the_matrix_so_obtained_is_k-times_the_determinant_of_the_original_matrix\" >If the elements of a row (column) of a matrix are multiplied by the same number , say k, the determinant of the matrix so obtained is k-times the determinant of the original matrix.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/swatilathia.com\/?page_id=2326\/#If_the_elements_of_any_row_or_column_of_determinant_are_sum_difference_of_two_or_more_elements_then_the_determinant_can_be_expressed_as_sum_difference_of_two_or_more_determinants\" >If the elements of any row or column of determinant are sum (difference) of two or more elements, then the determinant can be expressed as sum (difference) of two or more determinants.<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/swatilathia.com\/?page_id=2326\/#Solve_2_x_2_order_Determinant\" >Solve : 2 x 2 order Determinant<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/swatilathia.com\/?page_id=2326\/#Solve_3_x_3_order_Determinant\" >Solve : 3 x 3 order Determinant<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/swatilathia.com\/?page_id=2326\/#What_is_Cramers_Rule\" >What is Cramer\u2019s Rule ?<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/swatilathia.com\/?page_id=2326\/#Cramers_Rule_for_solving_2_x_2_Order_Determinant\" >Cramer\u2019s Rule for solving 2 x 2 Order Determinant<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/swatilathia.com\/?page_id=2326\/#Cramers_Rule_for_solving_3_x_3_Order_Determinant\" >Cramer\u2019s Rule for solving 3 x 3 Order Determinant<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Determinant_of_a_Matrix\"><\/span>Determinant of a Matrix<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"has-medium-font-size\">A matrix\u2019s determinant is the scalar value or number calculated using a square matrix. The square matrix could be 2 x 2, 3 x 3, 4 x 4, or any other type where the number of columns and rows are equal, such as n x n.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">A matrix\u2019s determinant is represented by two vertical lines or simply by writing det and the matrix name. For example, |A|, det(A), det A.<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"zak-oembed-container\"><div class=\"jetpack-video-wrapper\"><iframe loading=\"lazy\" title=\"Determinants | Introduction | What is Determinant?\" width=\"812\" height=\"457\" src=\"https:\/\/www.youtube.com\/embed\/wsEj-ZFftqM?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/div><\/div>\n<\/div><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Properties_of_Determinants\"><\/span>Properties of Determinants<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"If_the_rows_of_a_determinant_are_changed_into_columns_and_vice_verse_the_value_of_the_determinant_remains_unchanged_ie_A_At\"><\/span>If the rows of a determinant are changed into columns and vice verse, the value of the determinant remains unchanged. i.e. |A| = |A<sup>t<\/sup>|<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"zak-oembed-container\"><div class=\"jetpack-video-wrapper\"><iframe loading=\"lazy\" title=\"Determinant's Property No 1 | Determinant\" width=\"812\" height=\"457\" src=\"https:\/\/www.youtube.com\/embed\/g4n_PycttSI?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/div><\/div>\n<\/div><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"If_any_two_rows_or_columns_are_interchanged_the_value_of_the_resulting_determinant_is_additive_inverse_of_the_value_of_the_original_determinant_ie_A_-A\"><\/span>If any two rows (or columns) are interchanged, the value of the resulting determinant is additive inverse of the value of the original determinant. i.e. |A| = -|A|<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"zak-oembed-container\"><div class=\"jetpack-video-wrapper\"><iframe loading=\"lazy\" title=\"Determinant's Property No 2 | Determinant\" width=\"812\" height=\"457\" src=\"https:\/\/www.youtube.com\/embed\/NdCXgBxg0f0?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/div><\/div>\n<\/div><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"If_any_two_rows_or_columns_of_the_determinant_are_identical_the_determinants_value_is_zero\"><\/span>If any two rows or columns of the determinant are identical, the determinant\u2019s value is zero.<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"zak-oembed-container\"><div class=\"jetpack-video-wrapper\"><iframe loading=\"lazy\" title=\"Determinant's Property No 3 | Determinant\" width=\"812\" height=\"457\" src=\"https:\/\/www.youtube.com\/embed\/USKgHvPpA-o?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/div><\/div>\n<\/div><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"If_the_elements_of_a_row_or_column_of_a_determinant_are_added_subtracted_k-times_the_corresponding_elements_of_another_row_column_the_value_of_the_determinant_so_obtained_remains_unchanged\"><\/span>If the elements of a row (or column) of a determinant are added (subtracted) k-times the corresponding elements of another row (column), the value of the determinant so obtained remains unchanged.<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"zak-oembed-container\"><div class=\"jetpack-video-wrapper\"><iframe loading=\"lazy\" title=\"Determinant's Property No 4 | Determinant\" width=\"812\" height=\"457\" src=\"https:\/\/www.youtube.com\/embed\/Kin_cCfh-to?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/div><\/div>\n<\/div><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"If_the_elements_of_a_row_column_of_a_matrix_are_multiplied_by_the_same_number_say_k_the_determinant_of_the_matrix_so_obtained_is_k-times_the_determinant_of_the_original_matrix\"><\/span>If the elements of a row (column) of a matrix are multiplied by the same number , say k, the determinant of the matrix so obtained is k-times the determinant of the original matrix.<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"zak-oembed-container\"><div class=\"jetpack-video-wrapper\"><iframe loading=\"lazy\" title=\"Determinant's Property No 5 | Determinant\" width=\"812\" height=\"457\" src=\"https:\/\/www.youtube.com\/embed\/TQWsowduyV8?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/div><\/div>\n<\/div><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"If_the_elements_of_any_row_or_column_of_determinant_are_sum_difference_of_two_or_more_elements_then_the_determinant_can_be_expressed_as_sum_difference_of_two_or_more_determinants\"><\/span>If the elements of any row or column of determinant are sum (difference) of two or more elements, then the determinant can be expressed as sum (difference) of two or more determinants.<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"zak-oembed-container\"><div class=\"jetpack-video-wrapper\"><iframe loading=\"lazy\" title=\"Determinant's Property No 6 | Determinant\" width=\"812\" height=\"457\" src=\"https:\/\/www.youtube.com\/embed\/CKL6HTWOZs8?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/div><\/div>\n<\/div><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Solve_2_x_2_order_Determinant\"><\/span>Solve : 2 x 2 order Determinant<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"zak-oembed-container\"><div class=\"jetpack-video-wrapper\"><iframe loading=\"lazy\" title=\"Determinants | Chapter 1 | 2X2 order determinants &amp; their examples\" width=\"812\" height=\"457\" src=\"https:\/\/www.youtube.com\/embed\/_N_gmSgkcZE?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/div><\/div>\n<\/div><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Solve_3_x_3_order_Determinant\"><\/span>Solve : 3 x 3 order Determinant<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"zak-oembed-container\"><div class=\"jetpack-video-wrapper\"><iframe loading=\"lazy\" title=\"Determinants | Chapter 1| 3x3 determinants &amp; their examples\" width=\"812\" height=\"457\" src=\"https:\/\/www.youtube.com\/embed\/Ow7Htbjt-jY?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/div><\/div>\n<\/div><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"What_is_Cramers_Rule\"><\/span>What is Cramer\u2019s Rule ?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"zak-oembed-container\"><div class=\"jetpack-video-wrapper\"><iframe loading=\"lazy\" title=\"Determinants | Chapter 1| Cramer's Rule\" width=\"812\" height=\"457\" src=\"https:\/\/www.youtube.com\/embed\/ZbzI-c9tYp0?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/div><\/div>\n<\/div><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Cramers_Rule_for_solving_2_x_2_Order_Determinant\"><\/span>Cramer\u2019s Rule for solving 2 x 2 Order Determinant<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"zak-oembed-container\"><div class=\"jetpack-video-wrapper\"><iframe loading=\"lazy\" title=\"Determinants | Chapter 1| Cramer's Rule &amp; Example 2 (2 x 2 System)\" width=\"812\" height=\"457\" src=\"https:\/\/www.youtube.com\/embed\/JJxydOz6QBQ?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/div><\/div>\n<\/div><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Cramers_Rule_for_solving_3_x_3_Order_Determinant\"><\/span>Cramer\u2019s Rule for solving 3 x 3 Order Determinant<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<div class=\"zak-oembed-container\"><div class=\"jetpack-video-wrapper\"><iframe loading=\"lazy\" title=\"Determinants | Chapter 1| Cramer's Rule to solve 3 x 3 System Linear Equations\" width=\"812\" height=\"457\" src=\"https:\/\/www.youtube.com\/embed\/g6BV960IbyY?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/div><\/div>\n<\/div><\/figure>\n<\/body>","protected":false},"excerpt":{"rendered":"<p>Determinant of a Matrix A matrix\u2019s determinant is the scalar value or number calculated using a square matrix. The square matrix could be 2 x 2, 3 x 3, 4 x 4, or any other type where the number of columns and rows are equal, such as n x n. A matrix\u2019s determinant is represented [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"zakra_page_container_layout":"customizer","zakra_page_sidebar_layout":"customizer","zakra_remove_content_margin":false,"zakra_sidebar":"customizer","zakra_transparent_header":"customizer","zakra_logo":0,"zakra_main_header_style":"default","zakra_menu_item_color":"","zakra_menu_item_hover_color":"","zakra_menu_item_active_color":"","zakra_menu_active_style":"","zakra_page_header":true,"om_disable_all_campaigns":false,"footnotes":""},"class_list":["post-2326","page","type-page","status-publish","hentry"],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/swatilathia.com\/index.php?rest_route=\/wp\/v2\/pages\/2326","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/swatilathia.com\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/swatilathia.com\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/swatilathia.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/swatilathia.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2326"}],"version-history":[{"count":7,"href":"https:\/\/swatilathia.com\/index.php?rest_route=\/wp\/v2\/pages\/2326\/revisions"}],"predecessor-version":[{"id":2585,"href":"https:\/\/swatilathia.com\/index.php?rest_route=\/wp\/v2\/pages\/2326\/revisions\/2585"}],"wp:attachment":[{"href":"https:\/\/swatilathia.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2326"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}