I didn't know how to write these two problems without the proper symbols so I scanned them.
For the first problem, compute a few powers of B by hand and look for a pattern. You won't find a single closed formula, but a repeating pattern that should become apparent once n = 7 or so.Originally Posted by mantis
For the second problem, find a fourth vector such that the new vector together with the three given here forms a triangular matrix. Think about why that is sufficient. You may have to rearrange the order of the three vectors given here just a little.