solutions_501_09 - <0[KPCQQ MATH 323—501 QUIZ 9 Fall...

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Unformatted text preview: <0 [KPCQQ MATH 323—501, QUIZ 9. Fall 2010 NAME ______ ______ ROW _____ ____ Show all steps for credit. Q1. (3 pts.) Solve .Y"=AY-,: Y(0)= 3 Where 4 A435). 2’, , 1,,“ - (( 2.41 “% V’ijégm 3) , " l I "‘ 3%: m (1‘) (,4 ’ 3 ’\ _.... a( ( ~l " 0 0 U , ' (x; 6‘ .‘>.€€~1"CL(f AF. (7:0 1 >~; ‘ Q2. (3 pts.) Find the eigenvalues and eigenvectors of A=(§;§). 3'& E’- (‘f 7—)}; xz”0>+‘la—:O~-O(«\—q) :0 k=l / .16: Z i) '9 :S(:>-fiL“ (":5 3:: e; ,3 3) +4: ,:(:>~’>(':;(:> Q3. (4 pts) Let A be an n x n matrix with an eigenvalue A. Prove that A + 1 is an eigenvalue for A + I. mu? 5| 4 MP k be (flak Ak'J-Xkl 4L“ <A+I>x=Ax+k=§x><+k=GH>X 7 '00 >44, «A M 843,4..u21ue oar Act; ...
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