202 CHAPTER 9. LINEAR TRANSFORMATIONS
44. 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 11 −1 1 03 1 1 23 3 0 3
xyzw
=
0000
.
45. Using Problem 44 find the general solution to the following linear system.1 1 0 11 −1 1 03 1 1 23 3 0 3
xyzw
=
1243
.
46. 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 −1 1 1
xyzw
=
0000
.
47. Using Problem 46 find the general solution to the following linear system.1 1 0 12 1 1 21 0 1 10 −1 1 1
xyzw
=
2−1−31
.
48. Find ker(A) for
A =
1 2 3 2 10 2 1 1 21 4 4 3 30 2 1 1 2
.
Recall ker(A) is just the set of solutions to Ax = 0. It is the solution space to thesystem Ax = 0.
49. Using Problem 48, find the general solution to the following linear system.
1 2 3 2 10 2 1 1 21 4 4 3 30 2 1 1 2
x1
x2
x3
x4
x5
=
117
187