Coordinates in the space of functions
Task number: 2544
In the space of real polynomials of degree at most four with the basis \(X=(x^4+x^3,\ x^3+x^2,\ x^2+x,\ x+1,\ x^4+1)\) determine coordinates \([f]_X\) of the following vectors \(f\):
Variant 1
\(f(x)=x^4-1\).
Variant 2
\(f(x)=x^4+x^3+x^2+x+1\).
Variant 3
\(f(x)=x^4+x^2+1\).
Variant 4
\(f(x)=x^3+x\).
