Microsoft Word - ECON2015 Tutorial Set 2 Final XXXXXXXXXXdocx 1 ECON2015:MathematicsforEconomicsI TutorialSet2(Units3to4)-(contributes 10%) Question1(30marks) a) Find the rank of...

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Microsoft Word - ECON2015 Tutorial Set 2 Final - 2021.docx 1 ECON2015:MathematicsforEconomicsI TutorialSet2(Units3to4)-(contributes 10%) Question1(30marks) a) Find the rank of Ensurethatyouexplainthestepstaken. (10marks) b) Findtheinverseof usingElementaryRowOperations Ensurethatyouexplainthestepstaken. (20marks) Question2(25marks) a) Let? = $ ? 1 1 1 ? −1 −1 1 ? ( (i) Computethevalueof???(?). (4marks) (ii) Forwhatvaluesofxwillthematrixbesingular? (2marks) b) Writedownthequadraticformthatcorrespondstothefollowingmatrix. $ 3 2 4 2 −1 −3 4 −3 1 ( (3marks) c) Examinewhetherthefollowingquadraticformsarepositivedefinite,negative definiteorindefinite. (i) ?(?) = 3?! + 2?? + 5?? + 7?! − 2?! (3marks) (ii) ?(?) = 2?! − 4?! + 10?? − 7?? − 11?? + 3?! (3marks) A= 1 −1 2 3 2 6 −8 1 5 3 −2 10 ⎛ ⎝ ⎜ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ⎟ A= 1 2 3 0 1 −1 1 2 1 ⎛ ⎝ ⎜ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ⎟ Question1AMarkingScheme • Explanationofeachstep–5marks • Workings–5marks Question1BMarkingScheme • Explanationofeachstep–5marks • Workings–15marks 2 d) Determinewhetherornotthefollowingmatrixisorthogonal.Justifyyour response. (4marks) ? = 1 √6 ; √3 1 √2 0 −2 √2 −√3 1 √2 < e) prove that the quadratic equation ?! − 3? = −2? holds true for ? = $ 5 −6 −6 −1 4 2 3 −6 −4 ( (6marks) e)="" prove="" that="" the="" quadratic="" equation="" !="" −="" 3?="−2?" holds="" true="" for="" =="" $="" 5="" −6="" −6="" −1="" 4="" 2="" 3="" −6="" −4="" (="" (6="">