M294F09WS_EigenvaluesSol

M294F09WS_EigenvaluesSol - Math 2940 Worksheet Ch 7...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Background image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 2940 Worksheet: Ch. 7 Eigenvalues and Eigenvectors November 5, 2009 (Q9 /tt74mg 1. Find all eigenvalues, with their multiplicities, for the matrix Zwi 0 C) C) fir/if": / ’71 23/, ff ] Effimr-tmw' z. 2 I 2, 1* A [ONION l—‘l—‘l—lo NNOO r» W M “M? W )('/~vl)(2r~~i){z.l) : [Z'~1)1//~xl fig? Wale/15L 2. Find the eigenvalues and eigenvectors of the matrix 5 l7 . Mr : [2"1 if", a MMair):/s~:,1>/v/~w2)m) will/Awlhyrflkwfxfllf14/357 MM“, 1,, fig»: 17” a mat—Van :9 W» 1.722272) flimsy Maw/W) ‘ ‘ ~ . - " 7.“ Wuth my tarrfingflim a, aljm, WJ will] n’? t a, v _ 4v w m W 52,. 4791472 52: Ariqu 3—) #7417 a? a»? @P-flfl)? u , v ~ " #312“:ng :7, p,;,?][,:7,[/,[§7% Mt w M 3. If A is a 2 X 2 matrix with trA = 1 and detA = —12, What are the eigenva ues o varying Ma/meé’mflc fl/MMg/y flaw/fiflMVLMfl ‘ It WM: 2 "-~ xiv/K aha/[Wm MW, (/zn- 4! W «3] 4. Suppose matrix A is similar to matrix B, (that is, AS = SB for some invertible matrix S, or equivalently, A = SBSJ). What is the relationship betWeen the eigenvalues of A and B? H b tth ' t 7 AL, I 1 fl ’Mb :11? jug ZelfSyiijSM/W mg V ' fl 7 47.09%! VF Avvirsi, 99 1’65”? all?” a Mgr“: SW =>I Eé‘""v”9= l/JriVL eigenvector '17. Is ’3 an eigenvector for A’l? If it is, what is the corresponding eigenvalue? MW e fliflvsflr/2v2e 721%"? af7;#”’7 6. Let A b as abov. Is 17 an eigevector i0 A5,?‘I‘f so, what is Rte associated eigenvalue? W .7 s M gran/@3722) erg/thg/rf/flgg/Q Mf/V r 5127 ,p" trademark" or ,, Wéz/r?‘ 7. Arguing geometrically, find all eigenvectors and eigenvalues of the linear transormations given. If possible, find a basis of 1R” consisting of eigenvectors. V r, ,. - “A 7 fl/' / I“ 7%, 9 ‘l (b) Orthogonal proje “7/21? 197117 v), A? v Na 7, if (an/Ml /0 L, ,flfrz 2:0 /=% a] i (“LEW/aways, L Mmp’canwééyé r/ g: 8. If 0 is an eigenvalue of a matrix A, how many linearly independent eigenvectors oes 55 so 7KW¢7MA4£MM¢ gal/a {fir/4) 7 9, Find all 2 X 2 matrices for which 61 is an eigenvector, Is the set of all such matrices a subspace of the set of all 2 x 2 matrices? If [it is, find a basis. jgfoflj W [if W Z M/Wfl’ #1 things; their only earthly possession is a small purse with a bit of gold dust. Each day they get together for the following bizarre bonding ritual: Each of them takes his purse and gives his gold away to thevtwo others, in equal parts. For example, if Abraham has 4 ounces one day, he will give 2 each m Benjamin and Chaim lit? a /M MMW a) If Abraham starts out with 6 ounces, Benjamin with 1 ounce, and Chaim with 2 ounces, find formulas for the amounts a(t), b(t), and 005) each will have after t distributions. 1 1 1 . w 6‘ (Hint: the vectors [1], [0 ] , and [—1] will be useful) W .. 1 —1 0 a i ‘9 " ‘77 a V; A a Hail/#567 (b) Who will have the ost gold after one year, t t is, after 365 distributions? f 1/ 2 b{'{)+ icy): 4/19” ' -a/f/l . aNW _» ‘ W 73% - J a) + am 3 MW) W i W”) W Maw M f (1/!) J; l [m] a”) m“) + s c . z a a (1‘ “it? . 3 j t. r if. agar édeVZ/gj . ,A WréfiW : bf m ‘ _ __. j G (g) 9% 7/0: Z jag/l, 706%) Z ""0 .1 a 0 A J 460‘ .21 /MI) 5 (' 4‘ ‘21 0 _. W m ,4 (74~/%v/o//2) :fl/flv/ll/ , / . ML .: Vzflf) ‘7 g fig M144” V/fl‘r’zojf/ m jW ‘ ‘ ,, *i ,I/ /‘ o‘/'/2 I .://' 7 - 5 z .- x a .2 J; We 0 , [Mg/q [/2 v (:2, l “ II / ya” 0 ~( y,» 2 4/ Vlt/L'o 0 o ‘ L z I > . m» ,_.. fl. fl “Km-M flfiwsv? , y , W /#.1 .-./_ ya ‘7? ,g; W¢Wflm mwymfl/fim WW 4’ 2 2/ 2,. ( q "’ I “I /‘ ‘~> "5, ~f> , L. / «,4 a v 570 mm w {9, M 47/74"; 992W“? //“(/{VZg/j 5%? L ) 2/ . {Va LC Mia; / awe/HM, fly M M259 cm flr/‘yzwr 9% ~W/ Ag [w WW )0 Lama/K, 34‘ ...
View Full Document

{[ snackBarMessage ]}

Page1 / 4

M294F09WS_EigenvaluesSol - Math 2940 Worksheet Ch 7...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online