Lin_Algebra_Short_Exam2a_Spring_2014.pdf - MAT 260 Code...

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Unformatted text preview: ! MAT 260 Code Last Name: Semester ISPRING Student # : Date 1 05.15.2014 Signature : Time 3 12530 3 QUESTIONS ON 2 PAGES , Duration :40 min TOTAL 30 POINTS ' ' 1 (10pm) Let T: R4 ——> R5, T(:r.. y,z w) (,0 cc+2y-— 2—111 0 O :1:— y) be alinear transformation. Find 5 = d1m(ker(T )) and t— — dim(in1(T)=). Justify your answer. lcw(T):O}/(x121%2w) 6 RH: x+92na~\w=0) x‘ago @ 7‘33, Ezza-Hw % 29% are, {4‘22— 1:} ‘39 ELM/T.) 1 5PM £03!) $‘0)) (51‘2033_);£ ) 23-23 @ f: (PE/:91 £3 $2.7M.Forwja_. @ 2.(10pt3) Let T : R4 —+ 1R4, T(:c,y,z,w) = (OJ), —2x,y — 2) be a linear transformation. Test whether T is a nilpotent transformation or not? Justify your answer. ' TL: (xlww 40,0, 0,11% T5(x,3‘a,w) = (0,0,0)? 2%?”3: 0) T2150 ([7) o. I’d/QB» trams. 3.(10pts) Suppose T : R3 ——> R3 is a linear transformation Whose matrix with respect to the stan- dard basis IS B Based on Change of Basis Theorem find the matrices P Q such that A: PBQ is the matrix ofTWith reSpect to{( (3, —2,1), (1, 1,2),(1,— 1, 2) )} and {(1 0, 1),( (,0 1,1), (1 O, 30)} F3. {8’1} Tin 2' £5} Etigf )4}: Ju CW=JA§GDME§60145(L> Jets xE’H‘E FRI) j} -— P 5Q M21? [A He 73, H F F, IF: 0 =JUFE(1)= [#12: "L @ My“) P:h§(l*7 j 2 (no o> wuoféumwféw + 9. Wm (C) 1:0.) -‘—‘ 35“!» {'0 1‘ "Ljuat fl (9 ((0 0) (0,0,9 2 J; 0,0,1} +J‘J3(ON 1) + .3 I \J I +8, : :L ,:o J\L+9,, -0 ca jig—1.1 J1,J—Jp,=0 :9 yr—O 3%.?! ft: 3.1 :20 aiti ) J‘Vj‘bg‘n Bas’i— ...
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