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LA SALLE / OTHER / MTH 24001 / What is augmented matrix?

What is augmented matrix?

What is augmented matrix?

Description

School: La Salle University
Department: OTHER
Course: Linear Algebra and Applications
Professor: Stephen andrilli
Term: Fall 2017
Tags: Math, Linear Algebra, Linear, LaSalleUniversity, and lasalle
Cost: 50
Name: MTH 240 Test 2 Study Guide
Description: Study guide for test 2 in MTH 240-01 with Professor Andrilli covering section 2.1-3.3 of the textbook
Uploaded: 10/01/2017
9 Pages 97 Views 1 Unlocks
Reviews


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"}.lst-kix_3rc4negld4rz-5 > li:before{content:"- "}.lst-kix_3rc4negld4rz-6 > li:before{content:"- "}.lst-kix_ovm4ske2q7xl-6 > li:before{content:"" counter(lst-ctn-kix_ovm4ske2q7xl-6,decimal) ". "}.lst-kix_ovm4ske2q7xl-8 > li:before{content:"" counter(lst-ctn-kix_ovm4ske2q7xl-8,lower-roman) ". "}.lst-kix_3rc4negld4rz-3 > li:before{content:"- "}.lst-kix_3rc4negld4rz-7 > li:before{content:"- "}.lst-kix_3rc4negld4rz-4 > li:before{content:"- "}ol.lst-kix_ujreyz9hq5ez-8.start{counter-reset:lst-ctn-kix_ujreyz9hq5ez-8 0}.lst-kix_ujreyz9hq5ez-0 > li{counter-increment:lst-ctn-kix_ujreyz9hq5ez-0}.lst-kix_h0xrjgy43eeb-2 > li{counter-increment:lst-ctn-kix_h0xrjgy43eeb-2}.lst-kix_3rc4negld4rz-1 > li:before{content:"- "}.lst-kix_3rc4negld4rz-2 > li:before{content:"- "}.lst-kix_vsqlnfl3pf5a-3 > li{counter-increment:lst-ctn-kix_vsqlnfl3pf5a-3}.lst-kix_3rc4negld4rz-0 > li:before{content:"- "}.lst-kix_h0xrjgy43eeb-8 > li{counter-increment:lst-ctn-kix_h0xrjgy43eeb-8}.lst-kix_vsqlnfl3pf5a-6 > li{counter-increment:lst-ctn-kix_vsqlnfl3pf5a-6}.lst-kix_4ybtgz69zry9-6 > li:before{content:"- "}.lst-kix_4ybtgz69zry9-8 > li:before{content:"- "}ol.lst-kix_h0xrjgy43eeb-2.start{counter-reset:lst-ctn-kix_h0xrjgy43eeb-2 0}ol.lst-kix_ovm4ske2q7xl-2.start{counter-reset:lst-ctn-kix_ovm4ske2q7xl-2 0}.lst-kix_4ybtgz69zry9-4 > li:before{content:"- "}.lst-kix_ujreyz9hq5ez-5 > li{counter-increment:lst-ctn-kix_ujreyz9hq5ez-5}.lst-kix_h0xrjgy43eeb-1 > li{counter-increment:lst-ctn-kix_h0xrjgy43eeb-1}ol.lst-kix_nhbgt3c7wrc-0.start{counter-reset:lst-ctn-kix_nhbgt3c7wrc-0 0}.lst-kix_ovm4ske2q7xl-2 > li{counter-increment:lst-ctn-kix_ovm4ske2q7xl-2}.lst-kix_4ybtgz69zry9-0 > li:before{content:"- "}ol.lst-kix_ovm4ske2q7xl-5.start{counter-reset:lst-ctn-kix_ovm4ske2q7xl-5 0}.lst-kix_ujreyz9hq5ez-4 > li{counter-increment:lst-ctn-kix_ujreyz9hq5ez-4}.lst-kix_ovm4ske2q7xl-3 > li:before{content:"" counter(lst-ctn-kix_ovm4ske2q7xl-3,decimal) ". "}.lst-kix_4ybtgz69zry9-2 > li:before{content:"- "}.lst-kix_ovm4ske2q7xl-5 > li:before{content:"" counter(lst-ctn-kix_ovm4ske2q7xl-5,lower-roman) ". "}.lst-kix_nhbgt3c7wrc-8 > li{counter-increment:lst-ctn-kix_nhbgt3c7wrc-8}ul.lst-kix_yxnfsadsxk5v-0{list-style-type:none}.lst-kix_ovm4ske2q7xl-4 > li{counter-increment:lst-ctn-kix_ovm4ske2q7xl-4}ul.lst-kix_yxnfsadsxk5v-6{list-style-type:none}ul.lst-kix_yxnfsadsxk5v-5{list-style-type:none}ul.lst-kix_yxnfsadsxk5v-8{list-style-type:none}.lst-kix_bjj9g5xqrip-1 > li:before{content:"- "}ul.lst-kix_yxnfsadsxk5v-7{list-style-type:none}.lst-kix_ovm4ske2q7xl-1 > li:before{content:"" counter(lst-ctn-kix_ovm4ske2q7xl-1,lower-latin) ". "}ul.lst-kix_yxnfsadsxk5v-2{list-style-type:none}ul.lst-kix_yxnfsadsxk5v-1{list-style-type:none}ul.lst-kix_yxnfsadsxk5v-4{list-style-type:none}.lst-kix_vsqlnfl3pf5a-2 > li{counter-increment:lst-ctn-kix_vsqlnfl3pf5a-2}ol.lst-kix_vsqlnfl3pf5a-6.start{counter-reset:lst-ctn-kix_vsqlnfl3pf5a-6 0}ul.lst-kix_yxnfsadsxk5v-3{list-style-type:none}ol.lst-kix_ovm4ske2q7xl-8{list-style-type:none}ol.lst-kix_ovm4ske2q7xl-6{list-style-type:none}.lst-kix_bjj9g5xqrip-5 > li:before{content:"- "}ol.lst-kix_ovm4ske2q7xl-7{list-style-type:none}ol.lst-kix_ovm4ske2q7xl-4{list-style-type:none}ol.lst-kix_ovm4ske2q7xl-5{list-style-type:none}.lst-kix_nhbgt3c7wrc-6 > li{counter-increment:lst-ctn-kix_nhbgt3c7wrc-6}ol.lst-kix_ovm4ske2q7xl-2{list-style-type:none}ol.lst-kix_ovm4ske2q7xl-3{list-style-type:none}ol.lst-kix_ovm4ske2q7xl-0{list-style-type:none}ol.lst-kix_ovm4ske2q7xl-1{list-style-type:none}ol.lst-kix_vsqlnfl3pf5a-3.start{counter-reset:lst-ctn-kix_vsqlnfl3pf5a-3 0}ol.lst-kix_ujreyz9hq5ez-0.start{counter-reset:lst-ctn-kix_ujreyz9hq5ez-0 0}.lst-kix_bjj9g5xqrip-3 > li:before{content:"- "}.lst-kix_vsqlnfl3pf5a-7 > li{counter-increment:lst-ctn-kix_vsqlnfl3pf5a-7}.lst-kix_vsqlnfl3pf5a-1 > li{counter-increment:lst-ctn-kix_vsqlnfl3pf5a-1}ol.lst-kix_h0xrjgy43eeb-0.start{counter-reset:lst-ctn-kix_h0xrjgy43eeb-0 0}.lst-kix_no6bfdtry1mg-3 > li:before{content:"- "}ol.lst-kix_ujreyz9hq5ez-8{list-style-type:none}ol.lst-kix_ujreyz9hq5ez-7{list-style-type:none}ol.lst-kix_ujreyz9hq5ez-6{list-style-type:none}ol.lst-kix_ujreyz9hq5ez-5{list-style-type:none}.lst-kix_nhbgt3c7wrc-1 > li:before{content:"" counter(lst-ctn-kix_nhbgt3c7wrc-1,lower-latin) ". "}ol.lst-kix_ujreyz9hq5ez-4{list-style-type:none}ol.lst-kix_ujreyz9hq5ez-3{list-style-type:none}ol.lst-kix_ujreyz9hq5ez-2{list-style-type:none}ol.lst-kix_ujreyz9hq5ez-1{list-style-type:none}.lst-kix_nhbgt3c7wrc-3 > li:before{content:"" counter(lst-ctn-kix_nhbgt3c7wrc-3,decimal) ". "}ol.lst-kix_ujreyz9hq5ez-0{list-style-type:none}.lst-kix_vsqlnfl3pf5a-8 > li{counter-increment:lst-ctn-kix_vsqlnfl3pf5a-8}.lst-kix_no6bfdtry1mg-5 > li:before{content:"- "}.lst-kix_nhbgt3c7wrc-5 > li:before{content:"" counter(lst-ctn-kix_nhbgt3c7wrc-5,lower-roman) ". "}.lst-kix_ujreyz9hq5ez-0 > li:before{content:"" counter(lst-ctn-kix_ujreyz9hq5ez-0,decimal) ". "}.lst-kix_no6bfdtry1mg-7 > li:before{content:"- "}ol.lst-kix_ovm4ske2q7xl-3.start{counter-reset:lst-ctn-kix_ovm4ske2q7xl-3 0}.lst-kix_h0xrjgy43eeb-0 > li{counter-increment:lst-ctn-kix_h0xrjgy43eeb-0}ol.lst-kix_h0xrjgy43eeb-1.start{counter-reset:lst-ctn-kix_h0xrjgy43eeb-1 0}.lst-kix_ujreyz9hq5ez-2 > li:before{content:"" counter(lst-ctn-kix_ujreyz9hq5ez-2,lower-roman) ". "}.lst-kix_ujreyz9hq5ez-4 > li:before{content:"" counter(lst-ctn-kix_ujreyz9hq5ez-4,lower-latin) ". "}.lst-kix_h0xrjgy43eeb-6 > li:before{content:"(" counter(lst-ctn-kix_h0xrjgy43eeb-6,lower-roman) ") "}.lst-kix_nhbgt3c7wrc-1 > li{counter-increment:lst-ctn-kix_nhbgt3c7wrc-1}.lst-kix_yxnfsadsxk5v-6 > li:before{content:"- "}.lst-kix_nhbgt3c7wrc-7 > li{counter-increment:lst-ctn-kix_nhbgt3c7wrc-7}.lst-kix_yxnfsadsxk5v-4 > li:before{content:"- "}.lst-kix_ujreyz9hq5ez-6 > li:before{content:"" counter(lst-ctn-kix_ujreyz9hq5ez-6,decimal) ". "}.lst-kix_h0xrjgy43eeb-2 > li:before{content:"" counter(lst-ctn-kix_h0xrjgy43eeb-2,decimal) ". "}.lst-kix_h0xrjgy43eeb-4 > li:before{content:"(" counter(lst-ctn-kix_h0xrjgy43eeb-4,decimal) ") "}.lst-kix_ovm4ske2q7xl-3 > li{counter-increment:lst-ctn-kix_ovm4ske2q7xl-3}.lst-kix_yxnfsadsxk5v-0 > li:before{content:"- "}.lst-kix_h0xrjgy43eeb-0 > li:before{content:"" counter(lst-ctn-kix_h0xrjgy43eeb-0,upper-roman) ". "}.lst-kix_yxnfsadsxk5v-2 > li:before{content:"- "}ol.lst-kix_vsqlnfl3pf5a-5.start{counter-reset:lst-ctn-kix_vsqlnfl3pf5a-5 0}.lst-kix_ujreyz9hq5ez-8 > li:before{content:"" counter(lst-ctn-kix_ujreyz9hq5ez-8,lower-roman) ". "}ol.lst-kix_vsqlnfl3pf5a-7.start{counter-reset:lst-ctn-kix_vsqlnfl3pf5a-7 0}.lst-kix_h0xrjgy43eeb-7 > li{counter-increment:lst-ctn-kix_h0xrjgy43eeb-7}.lst-kix_g3o9v5uf1ugv-6 > li:before{content:"- "}.lst-kix_g3o9v5uf1ugv-7 > li:before{content:"- "}.lst-kix_g3o9v5uf1ugv-8 > li:before{content:"- "}ol.lst-kix_ujreyz9hq5ez-4.start{counter-reset:lst-ctn-kix_ujreyz9hq5ez-4 0}.lst-kix_yxnfsadsxk5v-8 > li:before{content:"- "}.lst-kix_nhbgt3c7wrc-7 > li:before{content:"" counter(lst-ctn-kix_nhbgt3c7wrc-7,lower-latin) ". "}.lst-kix_ovm4ske2q7xl-7 > li{counter-increment:lst-ctn-kix_ovm4ske2q7xl-7}.lst-kix_nhbgt3c7wrc-8 > li:before{content:"" counter(lst-ctn-kix_nhbgt3c7wrc-8,lower-roman) ". "}.lst-kix_no6bfdtry1mg-1 > li:before{content:"- "}.lst-kix_nhbgt3c7wrc-3 > li{counter-increment:lst-ctn-kix_nhbgt3c7wrc-3}.lst-kix_vsqlnfl3pf5a-4 > li:before{content:"" counter(lst-ctn-kix_vsqlnfl3pf5a-4,lower-latin) ". "}.lst-kix_vsqlnfl3pf5a-5 > li:before{content:"" counter(lst-ctn-kix_vsqlnfl3pf5a-5,lower-roman) ". "}.lst-kix_g3o9v5uf1ugv-4 > li:before{content:"- "}.lst-kix_g3o9v5uf1ugv-5 > li:before{content:"- "}.lst-kix_no6bfdtry1mg-0 > li:before{content:"- "}.lst-kix_no6bfdtry1mg-2 > li:before{content:"- "}.lst-kix_vsqlnfl3pf5a-3 > li:before{content:"" counter(lst-ctn-kix_vsqlnfl3pf5a-3,decimal) ". "}.lst-kix_g3o9v5uf1ugv-3 > li:before{content:"- "}ol.lst-kix_nhbgt3c7wrc-7.start{counter-reset:lst-ctn-kix_nhbgt3c7wrc-7 0}ol.lst-kix_ovm4ske2q7xl-4.start{counter-reset:lst-ctn-kix_ovm4ske2q7xl-4 0}.lst-kix_vsqlnfl3pf5a-0 > li:before{content:"" counter(lst-ctn-kix_vsqlnfl3pf5a-0,decimal) ". "}.lst-kix_vsqlnfl3pf5a-1 > li:before{content:"" counter(lst-ctn-kix_vsqlnfl3pf5a-1,lower-latin) ". "}.lst-kix_g3o9v5uf1ugv-0 > li:before{content:"- "}.lst-kix_g3o9v5uf1ugv-1 > li:before{content:"- "}.lst-kix_vsqlnfl3pf5a-2 > li:before{content:"" counter(lst-ctn-kix_vsqlnfl3pf5a-2,lower-roman) ". "}.lst-kix_g3o9v5uf1ugv-2 > li:before{content:"- "}ol.lst-kix_vsqlnfl3pf5a-2.start{counter-reset:lst-ctn-kix_vsqlnfl3pf5a-2 0}ul.lst-kix_3rc4negld4rz-8{list-style-type:none}.lst-kix_ovm4ske2q7xl-5 > li{counter-increment:lst-ctn-kix_ovm4ske2q7xl-5}.lst-kix_nhbgt3c7wrc-5 > li{counter-increment:lst-ctn-kix_nhbgt3c7wrc-5}ul.lst-kix_3rc4negld4rz-7{list-style-type:none}ul.lst-kix_3rc4negld4rz-6{list-style-type:none}ul.lst-kix_3rc4negld4rz-5{list-style-type:none}ul.lst-kix_3rc4negld4rz-4{list-style-type:none}ul.lst-kix_3rc4negld4rz-3{list-style-type:none}ul.lst-kix_3rc4negld4rz-2{list-style-type:none}ul.lst-kix_3rc4negld4rz-1{list-style-type:none}ul.lst-kix_3rc4negld4rz-0{list-style-type:none}.lst-kix_vsqlnfl3pf5a-6 > li:before{content:"" counter(lst-ctn-kix_vsqlnfl3pf5a-6,decimal) ". "}ul.lst-kix_bjj9g5xqrip-8{list-style-type:none}ol.lst-kix_nhbgt3c7wrc-8.start{counter-reset:lst-ctn-kix_nhbgt3c7wrc-8 0}ul.lst-kix_bjj9g5xqrip-7{list-style-type:none}ul.lst-kix_bjj9g5xqrip-6{list-style-type:none}.lst-kix_vsqlnfl3pf5a-7 > li:before{content:"" counter(lst-ctn-kix_vsqlnfl3pf5a-7,lower-latin) ". "}ul.lst-kix_bjj9g5xqrip-1{list-style-type:none}ol.lst-kix_nhbgt3c7wrc-1.start{counter-reset:lst-ctn-kix_nhbgt3c7wrc-1 0}ul.lst-kix_bjj9g5xqrip-0{list-style-type:none}.lst-kix_vsqlnfl3pf5a-8 > li:before{content:"" counter(lst-ctn-kix_vsqlnfl3pf5a-8,lower-roman) ". "}ol.lst-kix_h0xrjgy43eeb-3.start{counter-reset:lst-ctn-kix_h0xrjgy43eeb-3 0}ul.lst-kix_bjj9g5xqrip-5{list-style-type:none}ul.lst-kix_bjj9g5xqrip-4{list-style-type:none}ul.lst-kix_bjj9g5xqrip-3{list-style-type:none}ul.lst-kix_bjj9g5xqrip-2{list-style-type:none}ol.lst-kix_vsqlnfl3pf5a-1.start{counter-reset:lst-ctn-kix_vsqlnfl3pf5a-1 0}.lst-kix_vsqlnfl3pf5a-0 > li{counter-increment:lst-ctn-kix_vsqlnfl3pf5a-0}ol.lst-kix_h0xrjgy43eeb-4.start{counter-reset:lst-ctn-kix_h0xrjgy43eeb-4 0}.lst-kix_ujreyz9hq5ez-3 > li{counter-increment:lst-ctn-kix_ujreyz9hq5ez-3}.lst-kix_h0xrjgy43eeb-5 > li{counter-increment:lst-ctn-kix_h0xrjgy43eeb-5}ol.lst-kix_nhbgt3c7wrc-2.start{counter-reset:lst-ctn-kix_nhbgt3c7wrc-2 0}.lst-kix_ujreyz9hq5ez-6 > li{counter-increment:lst-ctn-kix_ujreyz9hq5ez-6}ol.lst-kix_vsqlnfl3pf5a-8.start{counter-reset:lst-ctn-kix_vsqlnfl3pf5a-8 0}.lst-kix_4ybtgz69zry9-7 > li:before{content:"- "}.lst-kix_vsqlnfl3pf5a-4 > li{counter-increment:lst-ctn-kix_vsqlnfl3pf5a-4}.lst-kix_4ybtgz69zry9-5 > li:before{content:"- "}ol.lst-kix_nhbgt3c7wrc-3.start{counter-reset:lst-ctn-kix_nhbgt3c7wrc-3 0}ol.lst-kix_h0xrjgy43eeb-5.start{counter-reset:lst-ctn-kix_h0xrjgy43eeb-5 0}.lst-kix_4ybtgz69zry9-3 > li:before{content:"- "}.lst-kix_ovm4ske2q7xl-4 > li:before{content:"" counter(lst-ctn-kix_ovm4ske2q7xl-4,lower-latin) ". "}ol.lst-kix_nhbgt3c7wrc-6.start{counter-reset:lst-ctn-kix_nhbgt3c7wrc-6 0}.lst-kix_4ybtgz69zry9-1 > li:before{content:"- "}ol.lst-kix_h0xrjgy43eeb-8.start{counter-reset:lst-ctn-kix_h0xrjgy43eeb-8 0}.lst-kix_h0xrjgy43eeb-3 > li{counter-increment:lst-ctn-kix_h0xrjgy43eeb-3}.lst-kix_ovm4ske2q7xl-1 > li{counter-increment:lst-ctn-kix_ovm4ske2q7xl-1}.lst-kix_ovm4ske2q7xl-2 > li:before{content:"" counter(lst-ctn-kix_ovm4ske2q7xl-2,lower-roman) ". "}.lst-kix_vsqlnfl3pf5a-5 > li{counter-increment:lst-ctn-kix_vsqlnfl3pf5a-5}ol.lst-kix_ujreyz9hq5ez-6.start{counter-reset:lst-ctn-kix_ujreyz9hq5ez-6 0}.lst-kix_bjj9g5xqrip-0 > li:before{content:"- "}.lst-kix_ovm4ske2q7xl-0 > li:before{content:"" counter(lst-ctn-kix_ovm4ske2q7xl-0,decimal) ". "}ol.lst-kix_ujreyz9hq5ez-3.start{counter-reset:lst-ctn-kix_ujreyz9hq5ez-3 0}.lst-kix_bjj9g5xqrip-2 > li:before{content:"- "}.lst-kix_bjj9g5xqrip-6 > li:before{content:"- "}ol.lst-kix_ovm4ske2q7xl-7.start{counter-reset:lst-ctn-kix_ovm4ske2q7xl-7 0}ol.lst-kix_vsqlnfl3pf5a-0.start{counter-reset:lst-ctn-kix_vsqlnfl3pf5a-0 0}.lst-kix_bjj9g5xqrip-4 > li:before{content:"- "}.lst-kix_no6bfdtry1mg-8 > li:before{content:"- "}ol.lst-kix_nhbgt3c7wrc-5.start{counter-reset:lst-ctn-kix_nhbgt3c7wrc-5 0}.lst-kix_ujreyz9hq5ez-8 > li{counter-increment:lst-ctn-kix_ujreyz9hq5ez-8}ol.lst-kix_h0xrjgy43eeb-7.start{counter-reset:lst-ctn-kix_h0xrjgy43eeb-7 0}ol.lst-kix_ujreyz9hq5ez-5.start{counter-reset:lst-ctn-kix_ujreyz9hq5ez-5 0}.lst-kix_no6bfdtry1mg-4 > li:before{content:"- "}.lst-kix_nhbgt3c7wrc-0 > li:before{content:"" counter(lst-ctn-kix_nhbgt3c7wrc-0,decimal) ". "}.lst-kix_ujreyz9hq5ez-2 > li{counter-increment:lst-ctn-kix_ujreyz9hq5ez-2}.lst-kix_h0xrjgy43eeb-4 > li{counter-increment:lst-ctn-kix_h0xrjgy43eeb-4}.lst-kix_ujreyz9hq5ez-7 > li{counter-increment:lst-ctn-kix_ujreyz9hq5ez-7}.lst-kix_nhbgt3c7wrc-2 > li:before{content:"" counter(lst-ctn-kix_nhbgt3c7wrc-2,lower-roman) ". "}.lst-kix_ujreyz9hq5ez-1 > li{counter-increment:lst-ctn-kix_ujreyz9hq5ez-1}.lst-kix_nhbgt3c7wrc-6 > li:before{content:"" counter(lst-ctn-kix_nhbgt3c7wrc-6,decimal) ". "}.lst-kix_no6bfdtry1mg-6 > li:before{content:"- "}.lst-kix_ujreyz9hq5ez-1 > li:before{content:"" counter(lst-ctn-kix_ujreyz9hq5ez-1,lower-latin) ". "}.lst-kix_nhbgt3c7wrc-4 > li:before{content:"" counter(lst-ctn-kix_nhbgt3c7wrc-4,lower-latin) ". "}ol.lst-kix_ovm4ske2q7xl-8.start{counter-reset:lst-ctn-kix_ovm4ske2q7xl-8 0}ol.lst-kix_nhbgt3c7wrc-2{list-style-type:none}.lst-kix_ujreyz9hq5ez-3 > li:before{content:"" counter(lst-ctn-kix_ujreyz9hq5ez-3,decimal) ". "}ol.lst-kix_nhbgt3c7wrc-1{list-style-type:none}.lst-kix_yxnfsadsxk5v-7 > li:before{content:"- "}ol.lst-kix_nhbgt3c7wrc-4{list-style-type:none}ol.lst-kix_nhbgt3c7wrc-3{list-style-type:none}.lst-kix_h0xrjgy43eeb-5 > li:before{content:"(" counter(lst-ctn-kix_h0xrjgy43eeb-5,lower-latin) ") "}.lst-kix_yxnfsadsxk5v-5 > li:before{content:"- "}ol.lst-kix_nhbgt3c7wrc-0{list-style-type:none}.lst-kix_h0xrjgy43eeb-3 > li:before{content:"" counter(lst-ctn-kix_h0xrjgy43eeb-3,lower-latin) ") "}.lst-kix_nhbgt3c7wrc-4 > li{counter-increment:lst-ctn-kix_nhbgt3c7wrc-4}.lst-kix_yxnfsadsxk5v-3 > li:before{content:"- "}ol.lst-kix_nhbgt3c7wrc-6{list-style-type:none}.lst-kix_ujreyz9hq5ez-5 > li:before{content:"" counter(lst-ctn-kix_ujreyz9hq5ez-5,lower-roman) ". "}ol.lst-kix_nhbgt3c7wrc-5{list-style-type:none}ol.lst-kix_nhbgt3c7wrc-8{list-style-type:none}ol.lst-kix_nhbgt3c7wrc-7{list-style-type:none}.lst-kix_ovm4ske2q7xl-6 > li{counter-increment:lst-ctn-kix_ovm4ske2q7xl-6}ol.lst-kix_h0xrjgy43eeb-0{list-style-type:none}ol.lst-kix_h0xrjgy43eeb-1{list-style-type:none}.lst-kix_h0xrjgy43eeb-1 > li:before{content:"" counter(lst-ctn-kix_h0xrjgy43eeb-1,upper-latin) ". "}ol.lst-kix_h0xrjgy43eeb-2{list-style-type:none}ol.lst-kix_h0xrjgy43eeb-3{list-style-type:none}.lst-kix_yxnfsadsxk5v-1 > li:before{content:"- "}ol.lst-kix_h0xrjgy43eeb-4{list-style-type:none}.lst-kix_ovm4ske2q7xl-0 > li{counter-increment:lst-ctn-kix_ovm4ske2q7xl-0}ol.lst-kix_h0xrjgy43eeb-5{list-style-type:none}.lst-kix_ujreyz9hq5ez-7 > li:before{content:"" counter(lst-ctn-kix_ujreyz9hq5ez-7,lower-latin) ". "}ol.lst-kix_h0xrjgy43eeb-6{list-style-type:none}ol.lst-kix_h0xrjgy43eeb-7{list-style-type:none}ol.lst-kix_h0xrjgy43eeb-8{list-style-type:none}

Math 240 test number 2 - La Salle UniversityDon't forget about the age old question of Who are the key resources in business?

Section 2.1: Systems of linear equations

3 Row Operations: Gaussian Elimination

  1. Multiply any row by a nonzero number to create pivots
  2. Add any multiple of one row to another row to create zeros
  3. Switch any two rows

Augmented matrix [A|B]If you want to learn more check out What is the meaning of strategos?

Coefficient matrix Ax = BIf you want to learn more check out What kinds of issues can elasticity help us understand?

Number of solutions to a system:

  1. A single solution↘
  2. Infinite solutions → consistent system
  3. No solutions - inconsistent

If a column is not a pivot, its variable ERDon't forget about the age old question of What are the 4 major fields of anthropology?

Dependent variables = pivotsIf you want to learn more check out What does the proportion of income mean?

independent variables = no pivots

For inconsistent systems, the final augmented matrix always contains at least one row:We also discuss several other topics like What do you call the isomers with the same formula but different connectivity of atoms?

        [0 0,.. 0 | C] C  0

Of c = 0, ignore row and solve and solve system using back substitution

        Solution set = {(        ) | C E R}

Number 11         (a)T        (c)F        (e)T        (g)F

                (b)F        (d)F        (f)T

Section 2.2: Reduced Row Echelon Form

Row Echelon Form = staircase pattern of pivots

Gauss - Jordan Method

  • Zero out entries above each pivot as well
  • Fewer non zero numbers in final augmented matrix so solution set is more apparent

Reduced Row Echelon Form

  1. 1rst non zero number in each row is a 1
  2. Each successive row has its 1rst non zero number in a later column
  3. All entries above and below pivots are zero
  4. All full rows of zeros are in final rows

Homogeneous System: AX = 0 ← zero matrix

  • Augmented matrix [A | 0]
  • Never inconsistent, always consistent
  • Has 1 solution (trivial solutions) or infinite solutions (non trivial)

CORR 2.3 if a system of “m” equations and “n” unknowns is homogeneous and m < n, then there is an infinite number of solutions

  • “Zero” solutions never occurs

Application: balancing chemical equations

  • Empirical formula → coulis each element and created an augmented matrix solving several systems simultaneously
  • Augmented matrix [A | BC]

Number 14        (a)T        (c)F        (e)F

                (b)T        (d)T        (f)F

Section 2.3: Equivalent Systems

Two systems of “m” linear equations in “n” variables are equivalent if they have exactly the same solution set

A matrix C is row equivalent to a matrix D if D is obtained from C by a finite number of row operations, type (I), (II), and (III)

  • Every operation has a reversal
  1. <i> ← c <i>                         <i> ← <i>
  2. <i> ← c <i> + <j>                 <j> ← -c<i> + <j>
  3. <i> ↔ <i>                        <i> ↔ <j>

THM 2.4 (RE) = row equivalent

Let C,D,E be matrices of same size

  1. C (RE) D, so D (RE) C
  2. If C (RE) D and D (RE) E, then C (RE) E

THM 2.5 if Ax = B is a system of linear equations and if [A | B] is row equivalent to [C,D] then Cx = D is equivalent to Ax = B

  • Some solutions; justification for rref

THM 2.6 Every matrix is row equivalent to a unique rref matrix

Rank of matrix = number of pivot in the rref of the matrix

THM 2.7

If rank (A) < n = infinite solutions

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