Lin_Algebra_Short_Exam2b_Spring_2014.pdf - METU NCC LINEAR...

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Unformatted text preview: METU - NCC. LINEAR ALGEBRA _ SHORT EXAM 2 ‘ Code : MAT 260 Last Name: AcadYeari 2013—2014 Name ‘ Semester 3 SPRING Student # Date : 24.04.2014 Signature : Time = 17:49 , 3 QUESTIONS ON 2 PAGES Duration 1 40 mm TOTAL 30 POINTS III-II_'l-J’ 7 J Ir 1.{10pts) Let T : R4 —* R3 be the linear transformation defined as T(:c1,x2,:c3,x4) = ($1 + $2 + 333, 3:3 - 2:4, 331 + as; + :04). Find the dimensions of the image and the kernel of T. "1"" 4"” W“ I "h, _ W1: {ixhxflflxspxq I ><l+261+205-3/ x3 XLi (lflxo /O> (01'ij) are a- kwdvécforg in, Ice/("(T) ob; MfUzz >6: (°1)@50-)+ x5(:~—/)1/D hem/«AC— OW‘A \“f (MW Kthe WU) ,4 . V X (1,0 4‘64““ ”by? 2.(10pts) Let S = {a, 6}. Let T : 1198.2 -—+ FUN(S) be the lineer extension of T(l,_0) = Xe, + xb, T(0,1) = Xe - Xb- Show that T is an isomorphism. T(><,g)- WEE/ON 5%!) - XHqWE+ M ME:E E E E E . E OEJC‘V‘ (\WCTJE: O A 7— [3% 0w (BoerfiE/RB‘M; E 3.('10pt5) Find the matrix representation of T : R3 —+ 1R4, T(m1,sc2, x3) = (5121 + x2 + 51:3, 23:1 - 32:2, —3:;:,, 32:1 + 2:3) (with respect to the standard basis). el=(h0_‘0) 81,2599”? .95: [0’0'7 TEQQ,:EE'9VEOB> E 7(a) ‘= (”'E’O‘p) EU 1 i E U 0 TEE”: (“On—EEO O E I DZ 0‘ 50; ...
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