156 CHAPTER 8. MATRICES

37. Write

x1− x2 +2x3

2x3 + x1

3x3

3x4 +3x2 + x1

 in the form A

x1

x2

x3

x4

 where A is an appropriate matrix.

38. Write

x1 +3x2 +2x3

2x3 + x1

6x3

x4 +3x2 + x1

 in the form A

x1

x2

x3

x4

 where A is an appropriate matrix.

39. Write

x1 + x2 + x3

2x3 + x1 + x2

x3− x1

3x4 + x1

 in the form A

x1

x2

x3

x4

 where A is an appropriate matrix.

40. Using the inverse of the matrix, find the solution to the systems 1 0 32 3 41 0 2

 x

yz

 =

 123

 ,

 1 0 32 3 41 0 2

 x

yz

=

 210

 1 0 3

2 3 41 0 2

 x

yz

 =

 101

 ,

 1 0 32 3 41 0 2

 x

yz

=

 3−1−2

 .

Now give the solution in terms of a,b, and c to 1 0 32 3 41 0 2

 x

yz

=

 abc

 .

41. Using the inverse of the matrix, find the solution to the systems 1 0 32 3 41 0 2

 x

yz

 =

 123

 ,

 1 0 32 3 41 0 2

 x

yz

=

 210

 1 0 3

2 3 41 0 2

 x

yz

 =

 101

 ,

 1 0 32 3 41 0 2

 x

yz

=

 3−1−2

 .

Now give the solution in terms of a,b, and c to 1 0 32 3 41 0 2

 x

yz

=

 abc

 .