(b) let g be a graph on vertices , vn, and let a be its adjacency matrix. show that g is connected if and only if every entry of the matrix i+a+a^2 + a^n-1 is non-zero, where i is the n x n identity matrix.

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?