tut8_soln - Math 235 Tutorial 8 Problems 1: Classify the...

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Unformatted text preview: Math 235 Tutorial 8 Problems 1: Classify the following: a) [35 35] b) Q(a’r’) = 433% — 49315102 + 5:33 2: For Q(m1, 3:2, :53) = 5m? —4x1x2—8m1x3+8x§—4m2m3+5x§, determine the corresponding symmetric matrix A. By diagonalizing A, express 62(5) in diagonal form and give an orthogonal matrix that diagonalizes A. Classify Q. 3: Sketch the graph of 2x? + 4331962 ~ 30% = 4 showing both the original and new axes. Find the equation of the asymptotes. 4: Prove that if A is a positive definite symmetric matrix, then A is invertible. 5: Prove that if B is any invertible n x n matrix, then A = BTB is a positive definite symmetric matrix. Jew ,,,,,.~\A1 ~ "Rt-HA ‘3 A ) v “f \VEXV : 0-” 45 : 'X‘~—‘1_x+\42;i§ - y -— lk» 24+ , -: (H DOW) Lévw Va” "T; J?\ + “MA - rev‘th, 04> am: ._ 1w} fags A: Cr ~I “Z S V lam/44:): rm 11 ~1 S-X a (Hm-x) ~“f = (\L in +10” \~ f «fix H6 “f l :5) /\‘ : Z 4 Z L? \ :5 Cl _ if; )0 / L .2 2 L :3 Cl €05\\A‘w- (“NA \W 613(2)} & :5 I U(\LUU\OI\V.\ 7 mm‘k‘x 0mg Q U ;; 5~& ~$ AW" 'L g -1 “f "L Tic Aa\a«3:3 7) fA’fil: -—z ~—1 ’2. ~% «2 ~% V1 ‘5‘ ~2 1 ~% _0 'Z 5 o 3 «4 o ‘L «£9 31 '- A “I “‘9- NM (Ami) .~_" A5 {‘2 0‘ (\gm 'Eqrb 5‘ — 1 ~49 A '_V “i. g “L _* C) 4% (’1 I 0 _\ 1 0 ~\ ar~ 0 '2 ” \ 3‘) x1 «— 7‘3 :6 2.1! ~ 94> : G >‘7©\ wvfi k???) JP ‘ 9~+ ~z.*% ~——e l o O \ O D U z ‘- - L &(X\\-)C1‘¥‘>) : 5g § [xxxlw ESJQXB «r 39g ~‘6x1x3 +13% .CL‘N" (OCIGSEMJD W _ SDQA.M9‘\(\.3( MANY r A W V ”‘\ a“ ‘ A 3‘ V: r H "’ r : ‘5’) '3 V‘\ 18 LKLSO ,, 7 . \0 , f“ E93:0 ' "a r V §XL:\ 51> , ‘2 L AIL I Q n ; Eifil‘m V; WM i 1! ] iEtfich‘Q W1 L?- “\/+ ‘ 3, u"‘ 3f: 4,46”, ““ 35 f: V V} "J1 “v”; :5.» Les? F s 1/} 0 tit/w: m” «.3 My Wig“ Cw Cw with(plots) :A := W;B :: sqrt(3)—2~sqrt(2) sqrt(3)+2-sq11(2) A“ 2\/-3—+-\/—§‘ ° 5-H? f 7 1 B [3‘ + 2 5 ( ) implicitplot[[2 ~x2 + 4'x'y ——y2 = 4,y=—A-x,y=-B-x,y= %,y=-2-x],x=—5 ..5,y=—5 .5]; 4 f t § y .\ 4i 1 a 2 \ ' (\‘Ima‘x »\ \3 .. \K‘x N -4 -2 A 4 3 i 1"“ " / l/ // ‘\\ / \\ // _4 a m” 9 I \‘M ‘3" ~““"" I! - L C V) ( \ (2) E 4% ma \3 V”) (ii /,’. ’17 1‘ TI Ft cilawz L r‘\\\7 R‘s $24-$51 7 g [ET =,(9:)T \nMAéUe B §V)MM\“}‘: T ~ '7‘ So V} 53mm M ‘ c w ‘\ i ~10 W, ...
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This note was uploaded on 11/28/2011 for the course MATH 235 taught by Professor Celmin during the Fall '08 term at Waterloo.

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tut8_soln - Math 235 Tutorial 8 Problems 1: Classify the...

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