MATH204 FINAL EXAM WITH SOLUTIONS_DEC 2018.pdf - CONCORDIA...

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CONCORDIA UNIVERSITYDepartment of Mathematics&StatisticsCourseNumberSection(s)Mathematics204AllexceptECExaminationDatePagesFinalDecember 20182InstructorsCourse ExaminerAllE. CohenSpecial Instructions:[>Onlyapproved calculatorsareallowed.l>Justifyallyouranswers.[>Allquestionshave equal value.MARKS1.Use Cramer’srule tocomputethesolution ofthesystem:II’]+1‘223—3ml+2.13=0:1'22.173=2l0—22.Find theinverse ofthe matrixA2~1314,if it exists.2—343.Findall solutions ofthesystem:1:1+61'2+2273~51‘;2:175:—-421381:4:1152I5:—71305..._27134.Flnd the detemnnantofA12162345
MATH204Final ExaminationDecember2018Page2of25.a) Letu:(1, 5, —2).v=(3.—1.5).Find theorthogonal projectionofvonu.b) Letu':(2,3,1),1L22(3.1.2),1132(1.2.3). FindChe-2c;suchthat01U1+0211.2+C3U3=(1,0,1).6.a)Find theareaofa triangle withvertices(1,1,2),(0.1.4),(1. 2,5).Finda vector orthogonal to theplaneofthetriangle.b)Find the distancebetweenthepoint(2,—3)and theline21723y+<1.7.

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