In this unit, you will see that a vector space such as R2 has an infinite number of possible bases. What is the most challenging aspect of creating a...

In this unit, you will see that a vector space such as R2 has an infinite number of possible bases. What is the most challenging aspect of creating a non-standard basis for a vector space such as R2? Create a new basis for R2 that is not one of the bases for R2 presented in Section 4.4, and explain how you know it is a basis. Your basis may not have either of its vectors parallel to e1 or e2.