[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-523553-105":59,"doc-detail-523553-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","mutivariable-linear-systems-and-row-operations-systems-and-row-operations-write-augmented-matrices-solve-and-find-reduced-row-echelon-forms","Mutivariable Linear Systems and Row Operations - Systems and Row Operations - Write Augmented Matrices, Solve, and Find Reduced Row-Echelon Forms","","Worksheets on multivariable linear systems using augmented matrices and row operations. Students write the augmented matrix for given systems, then write the system of equations for each augmented matrix. The tasks include finding the reduced row-echelon form of each system and solving each system using Gaussian or Gauss-Jordan elimination, with final cases including solutions and “No solution” 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solution.”","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},523553,1791775343,{"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":29,"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},962090894170,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","Kuta Software-Infinite Precalculus Name   \nMutivariable Linear Systems and Row Operations  \nWrite the augmented matrix for each system of linear equations.  \nDate   \nPeriod   \n1) 􀀘x 􀀐 􀀕 y 􀀠 􀀐􀀙 2) 􀀐􀀖 x 􀀐 􀀗y 􀀠 􀀕􀀓  \n􀀐x 􀀎 􀀘 y 􀀠 􀀔􀀘 􀀖 x 􀀐 􀀘 y 􀀠 􀀕􀀘  \n3) x 􀀎 􀀖 y 􀀐 􀀕z 􀀠 􀀐􀀔􀀔 4) 􀀐􀀕x 􀀐 􀀗y 􀀐 􀀘z 􀀠 􀀔􀀔􀀐􀀕x 􀀐 􀀘 y 􀀎 􀀖z 􀀠 􀀔􀀚 􀀐x 􀀎 􀀗z 􀀠 􀀐􀀕􀀘  \n􀀗x 􀀐 z 􀀠 􀀔 􀀐􀀖 x 􀀐 􀀘 y 􀀎 z 􀀠 􀀐􀀕􀀘  \nWrite the system of linear equations for each augmented matrix.  \n􀀖 􀀗 􀀔 􀀐􀀘 􀀔 􀀐􀀔􀀙  \n5) 􀀐􀀖 􀀕  􀀕􀀖  6)  􀀔 􀀘  􀀐􀀕  \n􀀖 􀀐􀀔 􀀔 􀀛 􀀐􀀘 􀀐􀀗 􀀖  \n7)  􀀓 􀀐􀀔 􀀕 􀀐􀀔􀀓 8) 􀀔 􀀓 􀀗  \n􀀐􀀕 􀀕 􀀕 􀀐􀀛 􀀖 􀀐􀀘 􀀘  \n􀀐􀀛  \n􀀓  \n􀀐􀀔􀀓  \nFind the reduced row-echelon form for each system of linear equations.  \n9) 􀀘x 􀀐 􀀗y 􀀠 􀀐􀀔􀀓 10) 􀀗x 􀀐 􀀕 y 􀀠 􀀕  \n􀀐x 􀀎 y 􀀠 􀀕 􀀘x 􀀐 􀀕 y 􀀎 z 􀀠 􀀚  \n􀀖 x 􀀎 􀀗y 􀀐 z 􀀠 􀀖  \n11) x 􀀐 y 􀀎 􀀕z 􀀠 􀀐􀀔 12) 􀀖 x 􀀎 􀀖 y 􀀠 􀀐􀀔􀀕  \n􀀐􀀖 x 􀀎 􀀖 y 􀀎 􀀘z 􀀠 􀀖 􀀐􀀗x 􀀐 􀀕 y 􀀎 􀀕z 􀀠 􀀐􀀔􀀗  \n􀀕x 􀀐 􀀕 y 􀀠 􀀐􀀕 x 􀀎 􀀖 y 􀀎 􀀕z 􀀠 􀀔􀀔  \nSolve each system of linear equations using Gaussian or Gauss-Jordan elimination.  \n13) 􀀐􀀖 x 􀀐 􀀗y 􀀠 􀀐􀀘 14) 􀀕x 􀀎 􀀘 y 􀀎 z 􀀠 􀀐􀀔􀀕  \n􀀗x 􀀎 􀀖 y 􀀠 􀀜 􀀐x 􀀎 􀀗y 􀀎 􀀖z 􀀠 􀀐􀀗  \n􀀘x 􀀐 􀀕z 􀀠 􀀐􀀔􀀖  \n15) 􀀖 x 􀀎 􀀕 y 􀀐 􀀖z 􀀠 􀀔􀀖 16) 􀀐􀀕x 􀀐 􀀗y 􀀎 􀀗z 􀀠 􀀔􀀗  \n􀀗x 􀀎 􀀗z 􀀠 􀀔􀀕 􀀗x 􀀎 􀀕 y 􀀎 􀀗z 􀀠 􀀐􀀗  \n􀀐􀀕x 􀀐 y 􀀎 z 􀀠 􀀐􀀛 x 􀀎 􀀕z 􀀠 􀀐􀀕  \nKuta Software-Infinite Precalculus Name   \nMutivariable Linear Systems and Row Operations  \nWrite the augmented matrix for each system of linear equations.  \nDate   \nPeriod   \n1) 􀀘x 􀀐 􀀕 y 􀀠 􀀐􀀙  \n􀀐x 􀀎 􀀘 y 􀀠 􀀔􀀘  \n3) x 􀀎 􀀖 y 􀀐 􀀕z 􀀠 􀀐􀀔􀀔􀀐􀀕x 􀀐 􀀘 y 􀀎 􀀖z 􀀠 􀀔􀀚􀀗x 􀀐 z 􀀠 􀀔  \n􀀔  \n􀀐􀀕  \n􀀗  \n􀀖  \n􀀐􀀘  \n􀀓  \n􀀐􀀕  \n􀀖  \n􀀐􀀔  \n􀀐􀀔􀀔  \n􀀔􀀚  \n􀀔  \n2) 􀀐􀀖 x 􀀐 􀀗y 􀀠 􀀕􀀓  \n􀀖 x 􀀐 􀀘 y 􀀠 􀀕􀀘  \n4) 􀀐􀀕x 􀀐 􀀗y 􀀐 􀀘z 􀀠 􀀔􀀔  \n􀀐x 􀀎 􀀗z 􀀠 􀀐􀀕􀀘􀀐􀀖 x 􀀐 􀀘 y 􀀎 z 􀀠 􀀐􀀕􀀘  \nWrite the system of linear equations for each augmented matrix.  \n􀀖 􀀗 􀀔  \n5) 􀀐􀀖 􀀕  􀀕􀀖  \n􀀖 x 􀀎 􀀗y 􀀠 􀀔􀀐􀀖 x 􀀎 􀀕 y 􀀠 􀀕􀀖  \n􀀐􀀘 􀀔  \n6)  􀀔 􀀘  \n􀀐􀀔􀀙  \n􀀐􀀕  \n􀀐􀀘x 􀀎 y 􀀠 􀀐􀀔􀀙 x 􀀎 􀀘 y 􀀠 􀀐􀀕  \n􀀖 􀀐􀀔 􀀔 􀀛  \n7)  􀀓 􀀐􀀔 􀀕 􀀐􀀔􀀓  \n􀀐􀀕 􀀕 􀀕 􀀐􀀛  \n􀀖 x 􀀐 y 􀀎 z 􀀠 􀀛  \n􀀐 y 􀀎 􀀕z 􀀠 􀀐􀀔􀀓􀀐􀀕x 􀀎 􀀕 y 􀀎 􀀕z 􀀠 􀀐􀀛  \n􀀐􀀘 􀀐􀀗 􀀖 􀀐􀀛  \n8)  􀀔 􀀓 􀀗 􀀓  \n􀀖 􀀐􀀘 􀀘 􀀐􀀔􀀓  \n􀀐􀀘x 􀀐 􀀗y 􀀎 􀀖z 􀀠 􀀐􀀛 x 􀀎 􀀗z 􀀠 􀀓  \n􀀖 x 􀀐 􀀘 y 􀀎 􀀘z 􀀠 􀀐􀀔􀀓  \nFind the reduced row-echelon form for each system of linear equations.  \n9) 􀀘x 􀀐 􀀗y 􀀠 􀀐􀀔􀀓  \n􀀐x 􀀎 y 􀀠 􀀕  \n11) x 􀀐 y 􀀎 􀀕z 􀀠 􀀐􀀔􀀐􀀖 x 􀀎 􀀖 y 􀀎 􀀘z 􀀠 􀀖􀀕x 􀀐 􀀕 y 􀀠 􀀐􀀕  \n10) 􀀗x 􀀐 􀀕 y 􀀠 􀀕  \n􀀘x 􀀐 􀀕 y 􀀎 z 􀀠 􀀚  \n􀀖 x 􀀎 􀀗y 􀀐 z 􀀠 􀀖  \n12) 􀀖 x 􀀎 􀀖 y 􀀠 􀀐􀀔􀀕􀀐􀀗x 􀀐 􀀕 y 􀀎 􀀕z 􀀠 􀀐􀀔􀀗 x 􀀎 􀀖 y 􀀎 􀀕z 􀀠 􀀔􀀔  \nSolve each system of linear equations using Gaussian or Gauss-Jordan elimination.  \n13) 􀀐􀀖 x 􀀐 􀀗y 􀀠 􀀐􀀘  \n􀀗x 􀀎 􀀖 y 􀀠 􀀜  \n(􀀖 , 􀀐􀀔)  \n15) 􀀖 x 􀀎 􀀕 y 􀀐 􀀖z 􀀠 􀀔􀀖  \n􀀗x 􀀎 􀀗z 􀀠 􀀔􀀕􀀐􀀕x 􀀐 y 􀀎 z 􀀠 􀀐􀀛  \n(􀀐z 􀀎 􀀖 , 􀀖z 􀀎 􀀕 , z)  \n14) 􀀕x 􀀎 􀀘 y 􀀎 z 􀀠 􀀐􀀔􀀕  \n􀀐x 􀀎 􀀗y 􀀎 􀀖z 􀀠 􀀐􀀗  \n􀀘x 􀀐 􀀕z 􀀠 􀀐􀀔􀀖  \n(􀀐􀀖 , 􀀐􀀔 , 􀀐􀀔)  \n16) 􀀐􀀕x 􀀐 􀀗y 􀀎 􀀗z 􀀠 􀀔􀀗  \n􀀗x 􀀎 􀀕 y 􀀎 􀀗z 􀀠 􀀐􀀗 x 􀀎 􀀕z 􀀠 􀀐􀀕  \nNo solution.  \nCreate your own worksheets like this one with Infinite Precalculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaitHYSlTxUc08","https://ap.wps.com/l/cbCaitHYSlTxUc08","pdf",28811,"English","# Write the augmented matrix\n## Write the system of linear equations\n# Find reduced row-echelon form\n# Solve using Gaussian or Gauss-Jordan elimination","[{\"question\":\"What is the first step in these exercises for each linear system?\",\"answer\":\"Write the augmented matrix for each system of linear equations.\"},{\"question\":\"How do you proceed after working with augmented matrices?\",\"answer\":\"Write the corresponding system of linear equations for each augmented matrix, then find the reduced row-echelon form for each system.\"},{\"question\":\"How are the systems solved in the worksheet?\",\"answer\":\"Solve each system of linear equations using Gaussian or Gauss-Jordan elimination, and identify cases such as “No solution.”\"}]","Mutivariable Linear Systems and Row Operations - Systems and Row Operations - Write Augmented Matrices, Solve, and Find Reduced Row-Echelon Forms | PDF",1791427002]