{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

tut8_soln

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

This preview shows pages 1–9. Sign up to view the full content.

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

View Full Document

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

View Full Document

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

View Full Document

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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, ...
View Full Document

{[ snackBarMessage ]}

### Page1 / 9

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

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online