Math 205B Quiz 07 page 1 11/20/2009 Name {V11U k-J rdunDn>
1.Wv,~ [iJV2~ [~landVF mNoo,~b~ [Tl ~
lA. Find xand ysuch that S={Vi, V2, Va} ronnan orthogonal set.
~Md UJ'[~'J ~ 0MP rn.[!]=o t1#j) [Z}U]" 0 jLJ~;
htCt/N.:-tiS; -LX=-0 r4/VO 7x +IS-8"=0AND -'X ,.]", +'ir: =- 0,
~/.'.C";1
IE. Find a unit veetor in the direetion of VI. ftw' JIWS~.~ ~rIS' x-=-( ,;' 11~'" rt'#llith? 4" WJe:...!.;
t/fnJ~j~!b!v,! -j t'"+ s2-t(-Z)' ,,/YN{'V ~Iii .r- ttIP1~" ~t,
lC. Using the fad that the set Sis anorthog;onal basis ofR3, use dot product.".!to find the weight ofvz when b is written
as a linear oombination of {Vi, Vz,Va}. Show all your work.
-It- btf«'<tM ;r ;!t i/e!;;hlb
/.> )
O'({
v. .. V~
z~tnDi
PJ IJ" /+/+/
/S'-t?-'1 ~!! =@
J
[
3 9 6 12
1
1 4 2 5
2. Let Q= 2 7 4 9 .
3 11 6 14
2A. Find a basis B1 for CoI(Q).
rret (Q) '"
l
~ ~
0 0 0
0 0 ()
2E. Find a basis 82 for Col( Q)-L.
UK~ /l.; ?/ (t?) J. := ;./u/ (QT) ~ve ~;; ~i{ £/tJi(ry1
!JvJ/rri( Qr) "rf !!;]~(i L,JJA/vl(cr r) ~
OCJo () j [nJ~]
2C. Verifythat each membe"of B, is peq>endiculacto each member of B2. La--. Lf ,/.ff~ Jf, 4:
[
~
][
-~
J
'
[
1
J1
~~
1[
~
]f
'~
J[
q
]!
-~
~
i.'i "J(-Y;)"-I +~.. 0i' -f =-1-2'°'3 ~. ',' ~-)-1+1,D ;. ~~~-H~.II
=-1 1.,..2 ;::..D/ 1 I -::::0/ II 0 -00/ II {- 0/