in define for scalars .
- Compute the components of .
- Prove that if then .
- Find values of the scalars such that .
- Prove that there is no set of values for such that .
- The components of are
- Proof. If then we have
From the third equation and we have , and then the first equation implies . Hence, we must have
- If then we have
Since and we must have . Then since we have . Therefore, are values such that .
- If then we must have
But, and implies . Then, would implies . However, then we run into a contradiction since