Math 205B Quiz 01 page 1 09/18/2009 Name S~J.rf1o) .!iJ/uhOfJ
1. Considerthe augmentedmatrixA= [1~ ;~ 13~ ].
IA. What system of linear equations is r
cresented by -:
G;x, +I1Xz.-g
ID"J.,+ 2.0xz.. -::.30
lB. Fi:q.dthe reduced row echelon form (rref) of A by hand, showing all the matrices produced along the way. Say what
each elementary row operation was used to produce each new matrix from
"t e previousone. J)
-rt. . 11(.)Ct"If. 1\ It'l kNltIJ't hIt: JuQIL VJ~ ('ref of AJ' /!.ere{ but: ODe:
J~ v..re fYVi, I 1J1"JItj!> II J
rG 13 /8]tz~lZfD [~13
)
f?lfj~(r,-0ft.) (0I/-IOJ
l'() zo 30 ~ IZ.JJ)I Z 3
~
SIJv.p r, ~~ [/ 2
/
]J
0 I -10 r,~r;-2v;.)
,. [IDZSJ
0I-10 ~#"i is
in rrt.!.
IC. What is the solution of the system in part 1A?
{X,:Z3 (if '" ~ '2-1<fl.", (<1,-10))
Xz.=-IO \1.
[
211312
]
2. Consider the system of equations whose augmented matrix is B= 1 0 5 7 .
3 4 27 12
Find all the solutions of the system using the methods and notation we've developed in class. If there are no solutions,
explain why. Otherwise, give a specific solution and show it satisfies the first equation the augmented matrix represents.
(Use your calculator to find rref(B)). .
[
I05"
I
0].-J /, ,j. It .»tJ.
rref(B) Vrq Ca/l-v/ttlvr V:J 0 I 3 0 7~ IWJ! ~wj11l1! fJ1ti'(/XrIrf6
000 I Jf) et2.(/~ C\ +0'(. 1- O)C = 1
'1M "(J ,,) I
t4tiJ. hM NS/lJ(/~(I. 7hV{ It.
fI(1,~J ,{b.~ :j ~(/~j r~rere,.,t:e'/Iy, 15
r,; /f,CC!?j';>WnC .
[
2 1 13 12 10
]
3. Now consider the system of equations whose augmented matrix is C=1 0 5 7 6 .
3 4 27 12 14
Again, find all the solutions of the system using the methods and notation we've developed in class. If there are no solutions,
explain why; otherwise, give a specific solution and show it satisfies the first equation the augmented matrix represents. (Use
your calculator to find the rref).
rref() ~Uff~;D ~.;L Jw,;,J; I t ;y>k(Y>rc.w bc
~ : (X, ::: 3Y --->X]
)<z.::-/0 -3;xJ
XJ ~ f((L
." I '><'1-= - Lf
r
XI -::: 21
Nat{ 0(1{ -rcJc.. solllhqy.. 0~b-kIAlt/ ty cLor) Xl = 1. j I~f4iJ ~ )<, .,.-13
1, ;L I'ltyb;' w<-fjhwe: 2.lh "(-13)"t"liQ)if<:1/4) :' :~
~J, to 58 -/1 + 13 -'1g = /0 ao (e'3VI're,(..,. '1
0
I
()
S
3
0