{"id":3558,"date":"2022-03-27T03:12:55","date_gmt":"2022-03-27T03:12:55","guid":{"rendered":"http:\/\/calculuscoaches.com\/?page_id=3558"},"modified":"2022-03-27T03:37:16","modified_gmt":"2022-03-27T03:37:16","slug":"linear-dependence-independence-for-functions-with-examples","status":"publish","type":"page","link":"https:\/\/calculuscoaches.com\/index.php\/linear-dependence-independence-for-functions-with-examples\/","title":{"rendered":"linear dependence\/independence for functions with examples"},"content":{"rendered":"\n<p><a href=\"http:\/\/calculuscoaches.com\/wp-content\/uploads\/2022\/03\/linear-independence-depence-of-functions-with-lots-of-graphs.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-3564 mBox\"  src=\"http:\/\/calculuscoaches.com\/wp-content\/uploads\/2022\/03\/linear-independence-depence-of-functions-with-lots-of-graphs.png\" alt=\"\" width=\"1839\" height=\"4306\" srcset=\"https:\/\/calculuscoaches.com\/wp-content\/uploads\/2022\/03\/linear-independence-depence-of-functions-with-lots-of-graphs.png 1839w, https:\/\/calculuscoaches.com\/wp-content\/uploads\/2022\/03\/linear-independence-depence-of-functions-with-lots-of-graphs-128x300.png 128w, https:\/\/calculuscoaches.com\/wp-content\/uploads\/2022\/03\/linear-independence-depence-of-functions-with-lots-of-graphs-644x1508.png 644w, https:\/\/calculuscoaches.com\/wp-content\/uploads\/2022\/03\/linear-independence-depence-of-functions-with-lots-of-graphs-768x1798.png 768w, https:\/\/calculuscoaches.com\/wp-content\/uploads\/2022\/03\/linear-independence-depence-of-functions-with-lots-of-graphs-656x1536.png 656w, https:\/\/calculuscoaches.com\/wp-content\/uploads\/2022\/03\/linear-independence-depence-of-functions-with-lots-of-graphs-875x2048.png 875w, https:\/\/calculuscoaches.com\/wp-content\/uploads\/2022\/03\/linear-independence-depence-of-functions-with-lots-of-graphs-600x1405.png 600w\" sizes=\"auto, (max-width: 767px) 89vw, (max-width: 1000px) 54vw, (max-width: 1071px) 543px, 580px\" \/><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":142,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-3558","page","type-page","status-publish","hentry"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 5.0.4 - aioseo.com -->\n\t<meta name=\"robots\" content=\"max-image-preview:large\" \/>\n\t<link rel=\"canonical\" href=\"https:\/\/calculuscoaches.com\/index.php\/linear-dependence-independence-for-functions-with-examples\/\" \/>\n\t\t<meta name=\"generator\" content=\"All in One SEO (AIOSEO) 5.0.4\" \/>\n\t\t<meta property=\"og:locale\" content=\"en_US\" \/>\n\t\t<meta property=\"og:site_name\" content=\"Calculus Coaches | helps with math problems\" \/>\n\t\t<meta property=\"og:type\" content=\"article\" \/>\n\t\t<meta property=\"og:title\" content=\"linear dependence\/independence for functions with examples | Calculus Coaches\" \/>\n\t\t<meta property=\"og:url\" content=\"https:\/\/calculuscoaches.com\/index.php\/linear-dependence-independence-for-functions-with-examples\/\" \/>\n\t\t<meta property=\"article:published_time\" content=\"2022-03-27T03:12:55+00:00\" \/>\n\t\t<meta property=\"article:modified_time\" content=\"2022-03-27T03:37:16+00:00\" \/>\n\t\t<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n\t\t<meta name=\"twitter:title\" content=\"linear dependence\/independence for functions with examples | Calculus Coaches\" \/>\n\t\t<script type=\"application\/ld+json\" class=\"aioseo-schema\">\n\t\t\t{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/calculuscoaches.com\\\/index.php\\\/linear-dependence-independence-for-functions-with-examples\\\/#breadcrumblist\",\"itemListElement\":[{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/calculuscoaches.com\\\/#listItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\\\/\\\/calculuscoaches.com\\\/\",\"nextItem\":{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/calculuscoaches.com\\\/index.php\\\/linear-dependence-independence-for-functions-with-examples\\\/#listItem\",\"name\":\"linear dependence\\\/independence for functions with examples\"}},{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/calculuscoaches.com\\\/index.php\\\/linear-dependence-independence-for-functions-with-examples\\\/#listItem\",\"position\":2,\"name\":\"linear dependence\\\/independence for functions with examples\",\"previousItem\":{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/calculuscoaches.com\\\/#listItem\",\"name\":\"Home\"}}]},{\"@type\":\"Organization\",\"@id\":\"https:\\\/\\\/calculuscoaches.com\\\/#organization\",\"name\":\"Calculus Coaches\",\"description\":\"helps with math problems\",\"url\":\"https:\\\/\\\/calculuscoaches.com\\\/\"},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/calculuscoaches.com\\\/index.php\\\/linear-dependence-independence-for-functions-with-examples\\\/#webpage\",\"url\":\"https:\\\/\\\/calculuscoaches.com\\\/index.php\\\/linear-dependence-independence-for-functions-with-examples\\\/\",\"name\":\"linear dependence\\\/independence for functions with examples | Calculus Coaches\",\"inLanguage\":\"en-US\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/calculuscoaches.com\\\/#website\"},\"breadcrumb\":{\"@id\":\"https:\\\/\\\/calculuscoaches.com\\\/index.php\\\/linear-dependence-independence-for-functions-with-examples\\\/#breadcrumblist\"},\"datePublished\":\"2022-03-27T03:12:55+00:00\",\"dateModified\":\"2022-03-27T03:37:16+00:00\"},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/calculuscoaches.com\\\/#website\",\"url\":\"https:\\\/\\\/calculuscoaches.com\\\/\",\"name\":\"Calculus Coaches\",\"description\":\"helps with math problems\",\"inLanguage\":\"en-US\",\"publisher\":{\"@id\":\"https:\\\/\\\/calculuscoaches.com\\\/#organization\"}}]}\n\t\t<\/script>\n\t\t<!-- All in One SEO -->\n\n","aioseo_head_json":{"title":"linear dependence\/independence for functions with examples | Calculus Coaches","description":"","canonical_url":"https:\/\/calculuscoaches.com\/index.php\/linear-dependence-independence-for-functions-with-examples\/","robots":"max-image-preview:large","keywords":"","webmasterTools":{"miscellaneous":""},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"BreadcrumbList","@id":"https:\/\/calculuscoaches.com\/index.php\/linear-dependence-independence-for-functions-with-examples\/#breadcrumblist","itemListElement":[{"@type":"ListItem","@id":"https:\/\/calculuscoaches.com\/#listItem","position":1,"name":"Home","item":"https:\/\/calculuscoaches.com\/","nextItem":{"@type":"ListItem","@id":"https:\/\/calculuscoaches.com\/index.php\/linear-dependence-independence-for-functions-with-examples\/#listItem","name":"linear dependence\/independence for functions with examples"}},{"@type":"ListItem","@id":"https:\/\/calculuscoaches.com\/index.php\/linear-dependence-independence-for-functions-with-examples\/#listItem","position":2,"name":"linear dependence\/independence for functions with examples","previousItem":{"@type":"ListItem","@id":"https:\/\/calculuscoaches.com\/#listItem","name":"Home"}}]},{"@type":"Organization","@id":"https:\/\/calculuscoaches.com\/#organization","name":"Calculus Coaches","description":"helps with math problems","url":"https:\/\/calculuscoaches.com\/"},{"@type":"WebPage","@id":"https:\/\/calculuscoaches.com\/index.php\/linear-dependence-independence-for-functions-with-examples\/#webpage","url":"https:\/\/calculuscoaches.com\/index.php\/linear-dependence-independence-for-functions-with-examples\/","name":"linear dependence\/independence for functions with examples | Calculus Coaches","inLanguage":"en-US","isPartOf":{"@id":"https:\/\/calculuscoaches.com\/#website"},"breadcrumb":{"@id":"https:\/\/calculuscoaches.com\/index.php\/linear-dependence-independence-for-functions-with-examples\/#breadcrumblist"},"datePublished":"2022-03-27T03:12:55+00:00","dateModified":"2022-03-27T03:37:16+00:00"},{"@type":"WebSite","@id":"https:\/\/calculuscoaches.com\/#website","url":"https:\/\/calculuscoaches.com\/","name":"Calculus Coaches","description":"helps with math problems","inLanguage":"en-US","publisher":{"@id":"https:\/\/calculuscoaches.com\/#organization"}}]},"og:locale":"en_US","og:site_name":"Calculus Coaches | helps with math problems","og:type":"article","og:title":"linear dependence\/independence for functions with examples | Calculus Coaches","og:url":"https:\/\/calculuscoaches.com\/index.php\/linear-dependence-independence-for-functions-with-examples\/","article:published_time":"2022-03-27T03:12:55+00:00","article:modified_time":"2022-03-27T03:37:16+00:00","twitter:card":"summary_large_image","twitter:title":"linear dependence\/independence for functions with examples | Calculus Coaches"},"aioseo_meta_data":{"post_id":"3558","title":null,"description":null,"keywords":null,"keyphrases":null,"primary_term":null,"canonical_url":null,"og_title":null,"og_description":null,"og_object_type":"default","og_image_type":"default","og_image_url":null,"og_image_width":null,"og_image_height":null,"og_image_custom_url":null,"og_image_custom_fields":null,"og_video":null,"og_custom_url":null,"og_article_section":null,"og_article_tags":null,"twitter_use_og":false,"twitter_card":"default","twitter_image_type":"default","twitter_image_url":null,"twitter_image_custom_url":null,"twitter_image_custom_fields":null,"twitter_title":null,"twitter_description":null,"schema":{"blockGraphs":[],"customGraphs":[],"default":{"data":{"Article":[],"Course":[],"Dataset":[],"FAQPage":[],"Movie":[],"Person":[],"Product":[],"ProductReview":[],"Car":[],"Recipe":[],"Service":[],"SoftwareApplication":[],"WebPage":[]},"graphName":"","isEnabled":true},"graphs":[]},"schema_type":"default","schema_type_options":null,"pillar_content":false,"robots_default":true,"robots_noindex":false,"robots_noarchive":false,"robots_nosnippet":false,"robots_nofollow":false,"robots_noimageindex":false,"robots_noodp":false,"robots_notranslate":false,"robots_max_snippet":null,"robots_max_videopreview":null,"robots_max_imagepreview":"large","priority":null,"frequency":null,"local_seo":null,"breadcrumb_settings":null,"limit_modified_date":false,"ai":null,"created":"2023-08-03 01:45:20","updated":"2025-06-04 04:34:46","seo_analyzer_scan_date":null,"focus_keyword":null,"additional_keywords":null,"truseo_locale":null},"aioseo_breadcrumb":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\t\t\t<a href=\"https:\/\/calculuscoaches.com\/\" title=\"Home\">Home<\/a>\n\t\t<\/span><span class=\"aioseo-breadcrumb-separator\">\u00bb<\/span><span class=\"aioseo-breadcrumb\">\n\t\t\tlinear dependence\/independence for functions with examples\n\t\t<\/span><\/div>","aioseo_breadcrumb_json":[{"label":"Home","link":"https:\/\/calculuscoaches.com\/"},{"label":"linear dependence\/independence for functions with examples","link":"https:\/\/calculuscoaches.com\/index.php\/linear-dependence-independence-for-functions-with-examples\/"}],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/calculuscoaches.com\/index.php\/wp-json\/wp\/v2\/pages\/3558","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/calculuscoaches.com\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/calculuscoaches.com\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/calculuscoaches.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/calculuscoaches.com\/index.php\/wp-json\/wp\/v2\/comments?post=3558"}],"version-history":[{"count":3,"href":"https:\/\/calculuscoaches.com\/index.php\/wp-json\/wp\/v2\/pages\/3558\/revisions"}],"predecessor-version":[{"id":3566,"href":"https:\/\/calculuscoaches.com\/index.php\/wp-json\/wp\/v2\/pages\/3558\/revisions\/3566"}],"wp:attachment":[{"href":"https:\/\/calculuscoaches.com\/index.php\/wp-json\/wp\/v2\/media?parent=3558"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}