1001 Algebra Problems.PDF

(Marvins-Underground-K-12) #1

  1. c.First, rewrite the system as the following
    equivalent matrix equation as in Problem 920:


.


Next, identify the following determinants to be
used in the application of Cramer’s Rule:

So, from Cramer’s rule, we have:

Thus, the solution is x= –^4265 ,y=  21 5.


  1. c.First, rewrite the system as the following
    equivalent matrix equation as in Problem 921:


.


Next, identify the following determinants to be
used in the application of Cramer’s rule:

So, from Cramer’s rule, we have:

Thus, the solution is x= –^15 ,y= ^252 .


  1. b.First, rewrite the system as the following
    equivalent matrix equation as in Problem 922:


.


Next, identify the following determinants to be
used in the application of Cramer’s rule:

So, from Cramer’s rule, we have:

Thus, the solution is x= –1,y= –^136 .


  1. a.First, rewrite the system as the following
    equivalent matrix equation as in Problem 923:


.


Next, identify the following determinants to be
used in the application of Cramer’s Rule:

So, from Cramer’s rule, we have:

Thus, the solution is x= 2,y= –4.

y===DDy – 28 – 4

x===DDx 24 2

D^0 ()() ( )( )


2


4


0


00 2 4 8



– –– – –


y== =

Dx==– 04 –^11 ()()()()–––41 01 4=

D==––^0211 ()()()() 01 –––21 2=


x
y

0


2


1


1


4


–– 0


>>>HH H= –


y===DDy^32 – 6 –^163

x===DDx –^66 – 1

D ()() ( )( )


2


12


2


4 24 12 2 32



y==––=

Dx==– 42 –^03 ()()()()–––23 40 6=

D== 122 –^03 ()()()()23 120 6–– =–


x
y

2


12


0


3


2


– 4


>>>HH H= –


y==DDy^225

x==DDx – 51

D^3 ()()()()


1


5


9


– 39 15 22



y==––– =

Dx==––^5912 ()()()() 52 –––91 1=–

D==– 13 –^12 ()()()()–––32 11 5=


x
y

3


1


1


2


5


9



>>>––HH H=


y==DDy 251

x==DDx 2546

D ()() ()( )


1


0


2


1 11 0 2 1



y==––=

Dx==–– 12 254 ()()()()–––– 225 1 4= 46

D==^1025 –^4 ()( ) ()( ) 125 ––0 4 25=


x
y

1


0


4


25


2


1


>>>––HH H=


ANSWERS & EXPLANATIONS–
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