LINEAR ALGEBRA (Math 211)
HW #10 (Due Wed. Nov. 1 )


$\textstyle \parbox{11cm}{{\bf 1.} For a parallelepiped $ABCDA'B'C'D'$\ in ${\ma... ...box{\bf z}\quad \mbox{(d)\ } -\mbox{\bf x}-\mbox{\bf y}\quad \end{displaymath}}$ $\textstyle \parbox{6.8cm}{\begin{displaymath} \mbox{\begin{picture} (150,100)(0... ...60,100){\mbox{$C'$}} \put(130,70){\mbox{$C$}} \end{picture}}\end{displaymath}}$



For the following sets of vectors determine whether they are linearly dependent, and if so find the linear dependence between them.


2. $\mbox{\bf x}=(1,2)$;          $\mbox{\bf y}=(-1,-3)$


3. $\mbox{\bf x}=(-3,2)$;         $\mbox{\bf y}=(1,10)$;         $\mbox{\bf z}=(4,-5)$.


4. $\mbox{\bf x}=(-3,4,2)$;         $\mbox{\bf y}=(7,-1,3)$;         $\mbox{\bf z}=(1,1,8)$.


5. $\mbox{\bf x}=(1,2,1)$;         $\mbox{\bf y}=(1,-1,1)$;         $\mbox{\bf z}=(1,3,1)$.


6. $\mbox{\bf x}=(0,1,2,-2)$;         $\mbox{\bf y}=(2,0,3,1)$;         $\mbox{\bf z}=(2,-1,1,3)$.