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?
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.