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
.