1001 Algebra Problems.PDF

Set 59 (Page 139)

929. c.First, rewrite the system as the following
     equivalent matrix equation as in Problem 913:

.

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= ^2131 ,y= ^1131 .

930. b.First, rewrite the system as the following
     equivalent matrix equation as in Problem 882:

.

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= a,y= b.

931. b.First, rewrite the system as the following
     equivalent matrix equation as in Problem 915:

.

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= –8,y= 6.

932. a.First, rewrite the system as the following
     equivalent matrix equation as in Problem 916:

.

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= –7,y= 5.

y===DDy –– 15 5

x===DDx –– 17 – 7

D^2 ()( ) ()()

12

(^1) 22 11 5

• y==–– =–

Dx==–^1213 ()() ( )() 11 ––23 7=

D==^2131 ()() ()() 21 –– 13 = 1

x

y

2

1

3

1

1

– 2

>>>HH H=

y===DDy –– 16 6

x===DDx –^81 – 8

D ()() ()()

1

2

4

y== 3 12 –– 24 = 6

Dx==^4223 ()() ()() 43 – 22 8=

D==^1223 ()() ()() 13 –– 22 = 1

x

y

a

b

1

2

2

>>> 3 HH H=

y===DDy b 1 b

x===DDx a 1 a

Dy== 01 ab ()() ()() 10 bab– =

Dx==ab 10 ()() ()()aba 10 – =

D==^1010 ()() ()() 11 – 00 1=

x

y

a

b

1

0

0

>>> 1 HH H=

y== =DDy –– 2226 1311

x== =DDx –– 2246 2311

Dy==– 13 28 ( )() ()()–– 38 12 =– 26

Dx==^2875 ()() ()() 25 –– 87 = 46

D ( )() ()()

3

1

7

5 35 17 22

–

==–– =–

x

y

3

1

7

5

2

8

>>>– HH H=

ANSWERS & EXPLANATIONS–