Suppose we have a linear transformation x? ax where
[1 3 9 2
a= 1 0 3 4
0 1 2 3
2 3 0 5] ( a is matrix form 4 by 4)
a. find all x? r4 with ax = 0 (if any). give your solution in parameterized form.
b. determine if
y= [3
3
1
2]
y is in the range of a.
c. do the columns of a span r4 ? how do you know?

Assume that there is a 11% rate of disk drive failure in a year. a. if all your computer data is stored on a hard disk drive with a copy stored on a second hard disk drive, what is the probability that during a year, you can avoid catastrophe with at least one working drive? b. if copies of all your computer data are stored on four independent hard disk drives, what is the probability that during a year, you can avoid catastrophe with at least one working drive?