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## Homework Statement

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?

## Homework Equations

## 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.