×
Log in to StudySoup
Get Full Access to Elementary Linear Algebra: A Matrix Approach - 2 Edition - Chapter 2.4 - Problem 61
Join StudySoup for FREE
Get Full Access to Elementary Linear Algebra: A Matrix Approach - 2 Edition - Chapter 2.4 - Problem 61

Already have an account? Login here
×
Reset your password

Solved: In Exercises 56- 63, a sysrem of linear equarions

Elementary Linear Algebra: A Matrix Approach | 2nd Edition | ISBN: 9780131871410 | Authors: Lawrence E. Spence ISBN: 9780131871410 187

Solution for problem 61 Chapter 2.4

Elementary Linear Algebra: A Matrix Approach | 2nd Edition

  • Textbook Solutions
  • 2901 Step-by-step solutions solved by professors and subject experts
  • Get 24/7 help from StudySoup virtual teaching assistants
Elementary Linear Algebra: A Matrix Approach | 2nd Edition | ISBN: 9780131871410 | Authors: Lawrence E. Spence

Elementary Linear Algebra: A Matrix Approach | 2nd Edition

4 5 1 238 Reviews
22
1
Problem 61

In Exercises 56- 63, a sysrem of linear equarions is given. (a) Wrire each sysrem as ammrix equarion Ax = b. (b) Show rlwr A is invertible. and find A- 1 (c) Use A- 1 ro solve each sysrem. +x3 =

Step-by-Step Solution:
Step 1 of 3

' ntlfi6r fb (-q, hr,,o lr,*niu, Mgtx' &xtt \s X-aYtt r.€iro) oFy \.[_z F.ltnor Aillt is Y -q,xls b2+ c olz = bQ = A2- (1. n.rrns Er,r,rpsp Definitiont-1.. ellipsisthesetofal,loi.nPs, {r,y},suehho.t the sofn thedi.stancestweetwopo'i,ncalled,efociof thelli,psconstant. The rnajor axisthe ari,s througfoci,. The rninor axastheo.ri,sraugth,centererpend,i,etothemajor *ri,s. The verticeofheelli,pse theointwhere thelli,'intersectsmajararis. 2.EeuarroNs (*-hl)'-ik)- k)':,1|(*-hh)z ,(y-k)'_,, n -(a-V---;;-^ o' -(y-a'-- Axisr x- qx ts Y-ax15 a)b, relatibetween 6r-- q'- c2 b2, a2 - c2 a,b,antc Center V) Ch, E) Ch, Foci (vt *C, k) (h, Y+ A Ih 'At K) Ch, v:4 Vertices (h+o, k) (-v\ + e) ,V (h- a, K) (h r K-q) Sketch Atov' ,--l L, rnr AV r) filho r v, Section Example2.L.Fi,ni|,uati,ofthcnni,epheibelow. Fo6: ;{ A') ,) x' Y- f -F 1 x 1--. 7l V: -b'o a' \ .. _)< A=4 lt= 2 XZ , Y2 : + tn6\\0r 4 rh, o(rs 2.2Fi,nthequati.anthcani,caphed' Example 1 (x -h)' cy- k)= lo 0r' - *t L\3,-z (x -3)' (q+e, 1o2' I qe a,=3 b r l rnlh0 y : (x -3)= ct--A-i )-*-- S -*-- I A I u-sT (Y+2/ l--t : I I _ __3 4tt-1.1 bo= o3- c* b'=b2* 1' Sect9.3 aO, 3t0* lb Example 2.Writeusilowecnsr)thformuforg'nthe elwithcenter .u,u""""s"m* ""aucen"""r,|'ti"'**'fu' o = 3b = | =Tr.{,";#=o,u'*,*! Example 2.Findthequatioftheelli.pse watth and, and,=; '' 3U(l-#} foci {-1,2) {3,2) - rr'!+'.\^,^-.. ,*l t)e+ (v*rte u* - q tri,',,'f = -q s-=l - , b^=5 q- b*= 4 Example2.5. "#i"* # c '--lb U^2*U dl= 4 x-0 elli,pse2/,i,r2r., t\2oci,,rtimajoraris,dm,inor aforhe ceffr;"'l(t, 4)lq## . +1)' {- 2)2 16 -0 1-I"o = t = 2 3:= .l 1t-''r-r(\-t,K1(r) .- \l'r,a (_l,{r)e(-t,"p) \__ t' 1{r {ut' Il,l;fi* )ac- \,2.,,rre) 1. Spclloru 9.2 Tnn PlRnror,a Definition L.l.A parabola isthe setaf allpoi,ntsP : (r,g), thatare equ,id,istant .froma fisedpoi,ntcalled tlrecus and afined li,ne called directrix. 2.EeuauoNS,a)0 Equation Vertex IFocus IDirectrix :4a(r (v - k)' - lt) (v-k)':-4atr-tt\ X= h+a :4a(y (* - h)' - k) .VTV PIY (*-h)':-a"(y-k) X= K+r'l 4+& +5 Example2.1.Sketch thep,,'Y':;'r1t., (x n)'. o 4ctt=-C=j $=-* Example2.2.Find, the eofthearabod*rn"abebw. U-a)'= 4(t+3 j v&r.!ex: c \,e (V-Q'= 4a0-t, 6r-l^- 4a(x+t -4 -+c,0 (o-;)a= 4a(-A+4 L'"hcn Ca)' = 4 6L,Ct) ",1:-. 0 /:4a-i- tzi - Example2.3.Fi,nd equatiofthearabouitlfocus1,-zand ueratr (11). 'PtvedYtx (x-h)" , ",(-h)n = - +a(V- o kt,,ri({} (x-D{= : * la cvv - r) ****f-f _+I_ !l[Ltuu It5.t,,(h,Y- =(t,-2) a=3) Example 2.Findtheequatiotheparabowi,th (-r, (1-2). focus -2)anduerter at 4a{x- h) .i (x rt ii (x*!) ((u:t --- Section 3 Example2.5Fi,nd,equat'ofonearabaw'ituerter1-2)anddi,rectri,r ,-rr. I I (9 -v)' = -a(x*h) I (v+r)'= +r) I -rbCx i Example 2.6.ndtheequatiofn,earabowi,foeus-1,-Z)and,;i,rectri,r U:3. I Dir v€l'ttr=(-l,i) - I (x -a A -h)*= - 4a (v -r) t.J\ (x+r)a= _t}(y-i) parabola r2:6ale2.7Fi,nd,focus,i,reanduerter of wi,theequat'ion h r 4 q-h):=2 +alv-, r..\ Y{r1 ry{a,o) \J / (x- -o)- *-+:- 0)^ = b (v 4et - b _ f - Drrr frcw.r, (o , ) 7 L cirr-- Y=- ,Z u =37 Example2.8Fi,ntlfacus,,irectrii'a\d thefiarabotaheequation 2(A+2)2:*+3 ( - 2) vrv*Lx y+ 3 2, #(vt2)r= * tq, -2) Fcr,.,ts (y+ 1, (o +*") -# v\vecrY = * {= x ,= *a Example 2.9.,nd,focus,,i,rectaer-terthearabola wi,equat'ion =o() (Y+Z)2--2r*3 fl::tr -v\^ -- - 1 a (x-r,) ^r=rr,*l I C./ 'ir"I\.x 6t *e)'. _Jy+,(y*;)r_ *,{y_i) v{t(x - (A u\ -4a -;" 7 ,-d) = ff: i

Step 2 of 3

Chapter 2.4, Problem 61 is Solved
Step 3 of 3

Textbook: Elementary Linear Algebra: A Matrix Approach
Edition: 2
Author: Lawrence E. Spence
ISBN: 9780131871410

Other solutions

People also purchased

Related chapters

Unlock Textbook Solution

Enter your email below to unlock your verified solution to:

Solved: In Exercises 56- 63, a sysrem of linear equarions