9.3. EXERCISES 201
37. Write the solution set of the following system as the span of vectors and find a basisfor the solution space of the following system. 0 −1 2
1 0 11 −2 5
x
yz
=
000
.
38. Using Problem 37 find the general solution to the following linear system. 0 −1 21 0 11 −2 5
x
yz
=
1−11
.
39. Write the solution set of the following system as the span of vectors and find a basisfor the solution space of the following system.
1 0 1 11 −1 1 03 −1 3 23 3 0 3
xyzw
=
0000
.
40. Using Problem 39 find the general solution to the following linear system.1 0 1 11 −1 1 03 −1 3 23 3 0 3
xyzw
=
1243
.
41. Write the solution set of the following system as the span of vectors and find a basisfor the solution space of the following system.
1 1 0 12 1 1 21 0 1 10 0 0 0
xyzw
=
0000
.
42. Using Problem 41 find the general solution to the following linear system.1 1 0 12 1 1 21 0 1 10 −1 1 1
xyzw
=
2−1−30
.
43. Give an example of a 3× 2 matrix with the property that the linear transformationdetermined by this matrix is one to one but not onto.