10. What is the kernel of the linear transformation
| A
| B.
| C.
|
| D.
| E.
|
Solution: The answer is C.
The equations that govern the kernel are
By inspection, the third equation is a linear combination of the first two, so the system is equivalent to
Solving for x and y in terms of z, x = z/11 and y = 4z/11. Thus elements of the kernel have the form