SAMPLE MIDTERM 1 WITH SOLUTIONS.pdf - MATH 204 2 IVIIDTERM...

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MATH204/2IVIIDTERMTESTAllquestions haveequal value..UsingtheGauss—Jordanmethod, find all the solutions ofthesystemofequations3$+6y~22 +u=52x+4y+2u+2v=023s+4y+z+3u+v=5.‘1—l0LetA:2011—20a)CalculateA”.b) Usingtheaboveresultsolvethesystem‘33—y:22:0+z=3:12—2y2—1.(Nomarksifyoudon’tusethe resultofpart(a).)lO21..21Ol.Calculate the determinantofthematrlxO1192l10Using Cramer’s rulesolvethesystem3:1:+2212y~2=‘—-12x—-y_=1.(Nomarksifyoudon’tuse Cramer’srule.)Letu=(2, —1,3)andvz: (3,—2,1).a)Find numbers:5andysuchthatrun+yv=(1,——2,~9).b) Showthatthereexistnonumbersa:and3/suchthatmu+yvm(1,2,~1).a)Findthe.cosine of theangle between thevectorsuz(2,-—l,1)andv2(1,l,——2).b)Find numbersa,b,csuchthatthepoints(at,y) intheplanethatare equidistantof thepoints(2,—1)and(3, 2)areexactly thepoints satisfying theequationart: 4-by=c.
MATH. 205:./.M.34V+K7—2?/+,a,7—5"24¢+447aha/6+2”-=0240‘+9‘7z+;/+3,¢o+/V’=5.35“R/0.5IRAQ/Q,._———26/oxa10>a$4/3/f5..——S.J/a0//0-3/</4—K;91%3J“(1/05‘-24/3/5‘—&R’+R3we}//-/;’5~/a0//f0Raeg00-—2~54“3%5‘———_.__99\0
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