104 CHAPTER 5. MATRICES
34. Let
A =
1 0 32 3 41 0 2
.
Find A−1 if possible. If A−1 does not exist, determine why.
35. Let
A =
1 2 32 1 44 5 10
.
Find A−1 if possible. If A−1 does not exist, determine why.
36. Let
A =
1 2 0 21 1 2 02 1 −3 21 2 1 2
Find A−1 if possible. If A−1 does not exist, determine why.
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
.