math254.sample.final

math254.sample.final - i t m - t l ' n n a aonsingular arix...

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9^^ pl" $i'''qJ f- I t - ll onsingular marix P such that P-rAP is i r,r=l -t -tl'nnaan r 3l diagonal. What is P-'AP? t2ool tar lo -r ol o) Lo o -ll l-2 0l tal (c) L -rJ Z-M-Ans: c l2ool 2 ol -rl [-r o-ll tcr 2l -l'isr,our rh".e = | I r r -r'1 P=l '1. . L-l tl '[; :] ro n'l (o L; _;l l--llt-Aas: d hnd 0p dimcnsion of tlrc cigcnspacc corrcsponding to thc cigcnvaluc 2 if l2ro0l f0 0 A=ln n ) tl' l' 'l 10002) _; I is diagonatizablc by computing P-|AP, nh€lr 3 ", [; ?] n, [3 l] rl il el ;l n'[3 | (c) 0,3,3 (a) o (d) 3 l--.llt-Ansr c (b) I (c) 4 (c) 2 4_, Find th" "ig"n"arucs or,oc symmcri",*, [i i i] (a) 0,0,0 (d) 3,3,3 l-M-Aos: b 5 . vr,l"n or u. following marices is gel 0 I (b) 0,0,3 (e) I, I, I (b) \/i _\/1 22 \/i \/1 00 (a) onhogonal? f l o r l-i o [r l-5 4 ll L5 5l "' [? -;] fr r'l -il Lr 1l l-M-An<: d (e) &u. J
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[r o -rl 6,. Find rhe characteristic equatron of the mamx | 0 I -2 | L' r ol (a) ir -2lr+4i-3=0 (b) 3rr-4lr-2i+ =0 (c) Ir - 2,\r-41 +3=0 (d) Ar+2^'?+31 -3=0 (e),\r-2lr-4i- 3=0 2-M-Ans: a (b) I 4 2 lb, Wt ictt of rhc following vcctor spaccs is nel isomorphic to Ra? (a\ Mzz O) Pr G) Mr.t (d) c[0,4] (c) Mt.t _ __ l-M-Ans: d ll, rind th".t ndard matrix forI = TroT,if T,: R2 e Rr, Tr (r, )) = (-1,, r + y) and 7r: R2 -r Rr, ?,(r, y) (y, r, y + x). l"l ol frr] l0 -11 rol 1o rl 'l Lr 0l
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math254.sample.final - i t m - t l ' n n a aonsingular arix...

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