8.8. EXERCISES 155

29. Let

A =

(0 15 3

).

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

30. Let

A =

(2 13 0

).

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

31. Let

A =

(2 14 2

).

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

32. 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.

33. Let

A =

 1 2 32 1 41 0 2

 .

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

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.