Consider the vectors
- Find satisfying . How many such solutions are there?
- Find such that and . How many such solutions are there?
- Let . For we must have
Therefore, we have the three equations,
From the first equation we have . From the second equation we then have . Since any value of then satisfies the third equation we have that is arbitrary. Letting we then have and . Hence, a solution is
There are infinitely many solutions since we can take any value for to obtain another solution.
- From part (a) we know that the vectors such that are of the form
for any value of . Then,
From part (a) we then have and . Hence, is the only solution.