[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-523551-105":59,"doc-detail-523551-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","matrix-inverses-and-determinants-worksheets-evaluate-determinants-and-find-inverses","Matrix Inverses and Determinants - Worksheets - Evaluate Determinants and Find Inverses","","Infinite Precalculus worksheet focused on evaluating determinants and using them to decide whether inverses exist for given matrices. Problems 1–8 ask students to compute determinants, while subsequent items require determining if an inverse exists and then finding the inverse for each specified matrix. Critical thinking questions extend the ideas to a parameterized matrix and request the x-values that make an inverse possible, plus an example of a 3×3 matrix with a given determinant.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/matrix-inverses-and-determinants-worksheets-evaluate-determinants-and-find-inverses/523551/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/matrix-inverses-and-determinants-worksheets-evaluate-determinants-and-find-inverses/523551.png","ImageObject",300,407,{"name":92,"@type":93},"ahduag","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-10","2026-10-08",true,{"@type":102,"interactionType":103,"userInteractionCount":44},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How do you decide whether an inverse exists for a matrix?","Question",{"text":112,"@type":113},"Check the determinant condition implied by the worksheet: if the determinant is nonzero, an inverse exists; if the determinant is zero, it does not.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What does the worksheet ask you to do with the determinants in Problems 1–8?",{"text":117,"@type":113},"Evaluate each determinant shown in the listed matrix expressions.",{"name":119,"@type":110,"acceptedAnswer":120},"What are the critical thinking questions about?",{"text":121,"@type":113},"They ask for the x-values that make a parameterized matrix M have an inverse, and they ask for an example of a 3×3 matrix whose determinant equals the specified value.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},523551,1791753755,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":44,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":19,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":52,"preview_page_count":4},3985747870414,"https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc","Kuta Software-Infinite Precalculus Name   \nMatrix Inverses and Determinants Date  Period   \nEvaluate each determinant.  \n􀀐􀀔 􀀕 􀀖 􀀘  \n1)  􀀔 􀀐􀀗  2)  􀀐􀀘 􀀐􀀕  \n􀀐􀀗 􀀗 􀀐􀀕 􀀖  \n3)  􀀐􀀘 􀀐􀀖  4)  􀀓 􀀘  \n􀀐􀀘 􀀕 􀀔 􀀐􀀘 􀀐􀀗 􀀔  \n5)  􀀔 􀀓 􀀓 6) 􀀐􀀖 􀀓 􀀘  \n􀀓 􀀗 􀀓 􀀐􀀔 􀀓 􀀖  \n􀀖 􀀖 􀀔 􀀐􀀕 􀀔 􀀐􀀕  \n7)  􀀐􀀖 􀀐􀀔 􀀐􀀖 8) 􀀓 􀀘 􀀐􀀘  \n􀀐􀀗 􀀐􀀖 􀀔 􀀓 􀀕 􀀐􀀘  \nFor each matrix state if an inverse exists.  \n9)  􀀔􀀓􀀓 􀀐􀀔􀀓  10)  􀀕􀀓 􀀔   \nFind the inverse of each matrix.  \n􀀐􀀖 􀀔 􀀐􀀖 􀀐􀀖  \n11)  􀀜 􀀐􀀔  12) 􀀐􀀗 􀀐􀀖  \n􀀐􀀗 􀀓 􀀖 􀀐􀀔  \n13) 􀀐􀀛 􀀐􀀔  14) 􀀐􀀕 􀀗  \nFor each matrix state if an inverse exists.  \n􀀕 􀀐􀀕 􀀘  \n15) 􀀐􀀕 􀀖 􀀐􀀕  \n􀀖 􀀐􀀙 􀀐􀀗  \n􀀕 􀀐􀀔 􀀖  \n16)  􀀔 􀀐􀀔 􀀐􀀖  \n􀀐􀀕 􀀓 􀀐􀀗  \nFind the inverse of each matrix.  \n􀀐􀀕 􀀘 􀀐􀀕  \n17) 􀀐􀀕 􀀕 􀀓  \n􀀐􀀖 􀀐􀀕 􀀕  \n􀀔 􀀔 􀀐􀀕  \n18) 􀀐􀀖 􀀐􀀕 􀀘  \n􀀐􀀙 􀀗 􀀗  \nCritical thinking questions:  \n19) For what value(s) of x does the matrix M have an inverse?  \nM 􀀠  \nx 􀀔􀀕 x 􀀎 􀀔  \n20) Give an example of a 3×3 matrix that has a determinant of 􀀔 .  \nKuta Software-Infinite Precalculus  \nMatrix Inverses and Determinants  \nEvaluate each determinant.  \n􀀐􀀔 􀀕  \n1)  􀀔 􀀐􀀗  2)  \n􀀕  \n􀀐􀀗 􀀗  \n3)  􀀐􀀘 􀀐􀀖  4)  \n􀀖􀀕  \n􀀐􀀘 􀀕 􀀔  \n5)  􀀔 􀀓 􀀓  6)  \n􀀓 􀀗 􀀓  \n􀀗  \n􀀖 􀀖 􀀔  \n7)  􀀐􀀖 􀀐􀀔 􀀐􀀖  8)  \n􀀐􀀗 􀀐􀀖 􀀔  \n􀀕􀀓  \nName  Date  Period   \n􀀖 􀀘  \n􀀐􀀘 􀀐􀀕  \n􀀔􀀜  \n􀀐􀀕 􀀖  \n􀀓 􀀘  \n􀀐􀀔􀀓  \n􀀐􀀘 􀀐􀀗 􀀔  \n􀀐􀀖 􀀓 􀀘􀀐􀀔 􀀓 􀀖􀀐􀀔􀀙  \n􀀐􀀕 􀀔 􀀐􀀕  \n􀀓 􀀘 􀀐􀀘  \n􀀓 􀀕 􀀐􀀘􀀖􀀓  \nFor each matrix state if an inverse exists.  \n􀀔􀀓 􀀐􀀔  \n9)  􀀓 􀀓  \nNo  \n􀀐􀀔􀀓 􀀘  \n10)  􀀐􀀕 􀀐􀀔  \nYes  \nFind the inverse of each matrix.  \n􀀐􀀕  \n17) 􀀐􀀕  \n􀀐􀀖  \n 􀀔   \n􀀐 􀂘  \n􀀛  \n􀀘  \n􀀕  \n􀀐􀀕  \n􀀗  \n􀀗  \n􀀔􀀓  \n􀀐􀀕  \n􀀓  \n􀀕  \n􀀐􀀙  \n􀀐􀀔􀀓  \n􀀐􀀔􀀜  \n􀀗  \n􀀗  \n􀀙  \nCritical thinking questions:  \n19) For what value(s) of x does the matrix M have an inverse?  \nx 􀀔  \nM 􀀠 􀀕 x 􀀎 􀀔  \nAll values except 􀀔 and 􀀐􀀕  \n􀀔  \n18) 􀀐􀀖  \n􀀐􀀙  \n 􀀔 􀂘  \n􀀕  \n􀀔  \n􀀐􀀕  \n􀀗  \n􀀐􀀕􀀛  \n􀀐􀀔􀀛  \n􀀐􀀕􀀗  \n􀀐􀀕  \n􀀘  \n􀀗  \n􀀐􀀔􀀕 􀀔  \n􀀐􀀛 􀀔  \n􀀐􀀔􀀓 􀀔  \n20) Give an example of a 3×3 matrix that has a determinant of 􀀔 .  \nCreate your own worksheets like this one with Infinite Precalculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaimxD1P48maQr","https://ap.wps.com/l/cbCaimxD1P48maQr","pdf",25202,"English","# Evaluate each determinant\n## Determine whether an inverse exists\n## Find the inverse of each matrix\n## Critical thinking questions","[{\"question\":\"How do you decide whether an inverse exists for a matrix?\",\"answer\":\"Check the determinant condition implied by the worksheet: if the determinant is nonzero, an inverse exists; if the determinant is zero, it does not.\"},{\"question\":\"What does the worksheet ask you to do with the determinants in Problems 1–8?\",\"answer\":\"Evaluate each determinant shown in the listed matrix expressions.\"},{\"question\":\"What are the critical thinking questions about?\",\"answer\":\"They ask for the x-values that make a parameterized matrix M have an inverse, and they ask for an example of a 3×3 matrix whose determinant equals the specified value.\"}]","Matrix Inverses and Determinants - Worksheets - Evaluate Determinants and Find Inverses | PDF",1791426999]