Math 205B Quiz 02 page 1 01/22/2010 Nanle ~.tclcJhb'"

Note: .On this quiz, use the appropriate notation (e.g. "vector hats") wherever appropriate. Also, show any rref's you

use in any problem that requires one.

1. Suppose that Ais a 4 x 6 matrix, and consider the matrix equation Ax =b.

IA. How many rows does Ahave? ~

IB. How many COhllIll1.'3does Ahave~ .

IC. The vector x belongs to Rio for what va.lue of h? (G)

ID. The vector b belongs to RP for what value of p? W

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3 1 1 5

1r

l

1[

3

J[

7

1

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2. Suppose that A=i~; ~ . Let z = ~., b = ~ and d = ~ .

Label colunm vectors of Aas at, a2, <13,and 34.

2A. Find the linear combination of al, a2, 3:3, and 34 represented by Az.

,Al '~

'} 1 \ .>

~7. '2.. ~

~I 3 8

(2. 4S"

\

I

II::

01[n+ 1[i] ~1[~} D[!J= mf'~i~l}Ii]

.{~(;A J"-r ~/. ~ ~!)

2B. Can b be expressed as a linear combina.tion of ai, a2, 3:3, and 34? Explain why or why not.

~,t.ll~l.fq J.:<,t.If ~AflJ/~ X.fo fl- e;r/~ IJ X -=1.::; .fO U!e V~

a..~J/!. rref(III/;') ~[~!~ ! ~l htr, t/..t QJw1~ 0)(, TOX~ <-0./0<" =1,

0 0 0 0nLit,;f ~/Il) dtJh~ .00. I)X:: t; ~ft, .Stj~ I

r. J t..> L..:> ~ .-> ~

W'tRl (fl 10 ~ #!!!a_c. jq"qz.,t:f.l,Ci<1.

2C. Find all solutions x of the matrix equation Ax =d.

JI(re rrt{(fJjd)== [~ 7 ~ : ~]

)CJ (7 I I -I

OO()D D

~/;1 filiI ()! -;L. ~ h£1tj rm:J4t1~)

I:: 2;;" X"\

Xl.: 2- X'1

xf"l- )elf'

:X., hfr It.t:..

2D Do the oohunnvectornof A'pan R'? E~ #(2 10 '" ~.fir em"f~ @~ rkYJtJ W .:

-taJ~ ~~~.~ :/7> Mik. ,t 'faA1~7 ~ce fj.; ~"t. ~i!:

11J-/wtrft~,,~: Fot' Pi" Ijrk~'fr,JV( tilt' ~1Mt fl,LCa'lfo, 1;:: ~,~se: f!.. IJ)(~ fo t/PM. .{i,(4'"

if' if 1/ )[

IC1 () j * l/' Ilkkti~ u.VhJ" ~ ~

It If' rre. I},1;: : ~ ~ ~ ~~IL/~fv~ *.., iO.:t. 0 (I.f: '. - if) I~::j' /110/"

/) 0,,()' .,. I.)r.. -' II I ,.fJ. h1k 1/1 ./CeYJ(A (() ilJr ( I

¥ 't f'W, Co/{/~II VtfM"~ fI".o . 11s .

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