18.3. EXERCISES 395

24. Let A =

(2 1−1 3

).Find A−1 if possible. If A−1 does not exist, determine why.

25. Let A =

(0 15 3

).Find A−1 if possible. If A−1 does not exist, determine why.

26. Let A =

(2 13 0

). Find A−1 if possible. If A−1 does not exist, determine why.

27. Let A =

(2 14 2

).Find A−1 if possible. If A−1 does not exist, determine why.

28. Let A be a 2× 2 matrix which has an inverse. Say A =

(a bc d

). Find a formula

for A−1 in terms of a,b,c,d.

29. Let

A =

 1 2 32 1 41 0 2

 .

Find A−1 if possible. If A−1 does not exist, determine why.

30. Let

A =

 1 0 32 3 41 0 2

 .

Find A−1 if possible. If A−1 does not exist, determine why.

31. Let

A =

 1 2 32 1 44 5 10

 .

Find A−1 if possible. If A−1 does not exist, determine why.

32. 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.

33. Write

x1 − x2 +2x3

2x3 + x13x3

3x4 +3x2 + x1

 in the form A

x1x2x3x4

 where A is an appropriate matrix.

34. Write

x1 +3x2 +2x3

2x3 + x16x3

x4 +3x2 + x1

 in the form A

x1x2x3x4

 where A is an appropriate matrix.