- b.Identify the following determinants to be
used in the application of Cramer’s rule for the
matrix equation :
So, from Cramer’s rule, we have:
Thus, the solution is x= 2,y= 3.
- d.Identify the following determinants to be
used in the application of Cramer’s rule for the
matrix equation :
Since applying Cramer’s rule requires that we
divide by Din order to determine x and y,we
can only conclude that the system has either
zero or infinitely many solutions. We must
consider the equations directly and manipu-
late them to determine which is the case. To
this end, as in Problem 925, subtracting the
second equation from the first equation yields
the false statement 0 = –3. From this, we con-
clude that the two lines must be parallel
(which can also be checked by graphing
them). Hence, the system has no solution.
- d.Identify the following determinants to be
used in the application of Cramer’s rule for the
matrix equation :
Since applying Cramer’s rule requires that we
divide by Din order to determine x and y,we
can conclude only that the system has either
zero or infinitely many solutions. We must
consider the equations directly and manipu-
late them to determine which is the case. To
this end, as in Problem 926, the second equa-
tion in the system is obtained by multiplying
both sides of the first equation by 3. The two
lines are identical, so the system has infinitely
many solutions.
- b.Identify the following determinants to be
used in the application of Cramer’s rule for
the matrix equation :
So, from Cramer’s rule, we have:
Thus, the solution is x= –1,y= 2.
y===DDy –– 12 2
x===DDx –^11 – 1
D ()()()()
1
1
1
1 11 1 1^2
–
–
–
y==–––––=
Dx==–– 11 01 ( )() ()( )––– 10 1 1 1=
D==–– 11 – 01 ()()()()––––– 10 1 1= 1
x
y
1
1
1
0
1
1
–
–
>>>––HH H=
D ()( ) ()()
3
9
3
y== 12 312 – 93 9=
Dx== 124 – –^26 ()()()()46 122 0–– –=
D==^39 – –^26 ()( ) ()( )36 92 0–– –=
x
y
3
9
2
6
4
12
–
>>>– HH H=
D^3 ()() ()( )
3
2
1
y==–^31 ––3 2 9=
Dx==– 12 22 ( )() ()()–– 22 12 =– 6
D==^3322 ()() ()() 32 – 23 0=
x
y
3
3
2
2
2
1
>>>HH H= –
y===DDy 13 3
x===DDx 12 2
D ( )() ()( )
1
2
2
1 11 2 2 3
––
y==–––=
Dx==– 12 –^01 ()()()()–––21 10 2=
D==– 21 –^01 ()()()()–––11 20 1=
x
y
1
2
0
1
2
1
–
–
>>>HH H= –
ANSWERS & EXPLANATIONS–
