1001 Algebra Problems.PDF

Set 58 (Page 137)

913. a.The solution to the matrix equation , where a, b, c, d, e,and fare real numbers, is

given by , provided that the inverse matrix on the right side exists. From Problem 881,

the given system can be written as the equivalent matrix equation. The solution is

therefore given by. Using the calculation for the inverse from Problem 897 yields the

following solution:

So, the solution of the system is x= ^2131 ,y= ^1131 .

914. c.The solution of this system is clearly x= a,y= b, without needing to go through the formal procedure
     of solving the matrix equation.


915. b.The solution to the matrix equation , where a, b, c, d, e,and fare real numbers, is

given by , provided that the inverse matrix on the right side exists. From Problem 883,

the given system can be written as the equivalent matrix equation. The solution is

therefore given by. Using the calculation for the inverse from Problem 899 yields the

following solution:

So, the solution of the system is x= –8,y= 6.

x

y

3

2

2

1

4

2

8

6

–

–

>> >>HHHH==–

x

y

4

2

1

2

2

3

• 1

  
  

  
  

  
  

  HHH=

  
  

  
  

  
  

  
  

x

y

1

2

2

3

4

>>>HH H= 2

x

y

a

c

b

d

e

f

• 1

  
  

  
  

  
  

  HHH=

  
  

  
  

  
  

  
  

a

c

b

d

x

y

e

>>>HH H= f

x

y

22

5

22

1

22

7

22

3

2

8

22

46

22

26

11

23

11

13

–

===

R

T

S

S

S

S

R

T

S

S

S

S

R

T

S

S

S

S

>>

V

X

W

W

W

W

V

X

W

W

W

W

V

X

W

W

W

W

HH

x

y

3

1

7

5

2

8

= – –^1

>> >HHH

x

y

3

1

7

5

2

8

– =

>>>HH H

x

y

a

c

b

d

e

f

• 1

  
  

  
  

  
  

  HHH=

  
  

  
  

  
  

  
  

a

c

b

d

x

y

e

>>>HH H= f

ANSWERS & EXPLANATIONS–