1. The problem statement, all variables and given/known data There is a standard basis, B = (1; z; z^2; z^3; z^4) where B is the basis of a R4[z] of real polynomials of at most degree 4. I need to find another basis B' for R4[z] such that no scalar multiple of an element in B appears as a basis vector in B' and also prove that this B' is a basis. Can any help with this please? 2. Relevant equations 3. The attempt at a solution I could only think to do a basis B'=(0,1,z,z^2,z^3) but no sure if this is correct.