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MATH 2022 Week03Worksheet
MATH 2022 Week 3 worksheet
QY Putm=
[55-56]
.
Over R,
#det M = -and
M' '
=
Over 217 ,
m=EEI=EiT,
det M= .and
M"
=
Why does M' ' not exist over ZL
, ,?
- ]
QY Solve
x + Z = O
y + z = o
x + y= 1
over R :
k::L:t
over 273 by converting previous solution :
-Why is there no solution over Zz ?
.
QY Solve the following homogeneous system
over Zz !
x,
t nz t Nz + ks = 0
a,+ nz it notas = o
se,
+ ×3 + ks = 0
se,+ xz try
= 0
after first row reducing the following matrix
to reduced row echelon form :
f :::::
i ::::D .
QYI Consider the system
n + y = 1
n + z =
7+1n +
XZ= 0
@1 Row reduce to row echelon form :
[ :: :p't'tI o X o
(b) Over R,for which X is the system
Ci ) inconsistent ? M'
-
? 17di ) having a unique solution
The solution becomes-
(c) What happens over 723 ?
(d) What happens over Zz ?
Q5/ Put x = ( i 2345 ) ( 678 910 ).
find 22 =
÷4=
5
L =
and complete the multiplication table :
1 L ×' £3 Lt
1
:÷L
How does this comparewith the addition
table for 125 ?
-The group G=k > is cyclic ? True False
Q6/Put L = C 123 )
, p= ( 45 )
,F- xp = (123×45)
find
z2=83 =
84 =
*6 =
and complete the multiplication table :
1 8 82 y'
y4
y5
1
8
:'y5
How does this comparewith the addition
table for 26 ?
-The group G=k
, p >is cyclic ? True False
Q7/Put L= C i 2) ( 34 )
, p = ( 1 3) C 24 ),
8 = Lp = ( 1 2) ( 3 4) ( 1 3) ( 24 ) =
Find x'
=p'
= 82 =
pr =
jx =
and complete the multiplication table :
1 × p 8
1
:8
How does this comparewith the composition
table for symmetries of the rectangle ?
-The group G=k
, p >is cyclic ? True False
Q8/ Consider polynomials with coefficients
from Zz={ oil }.
Put
F = { 0,1 ,r
,Ita }
.
Complete the addition table for f :
+ 0 I a Hk
0
:ltn
Complete the multiplication table for F if
(a) It ih=o 0 I a Ita
:
: aor
Cb ) ltntxhio0 I a Ita
:
: aWhich of (a) or (b) yields a field ? D