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Coordinates in the space of functions

Task number: 2544

In the space of real polynomials of degree at most four with the basis X=(x4+x3, x3+x2, x2+x, x+1, x4+1) determine coordinates [f]X of the following vectors f:

  • Variant 1

    f(x)=x41.

  • Variant 2

    f(x)=x4+x3+x2+x+1.

  • Variant 3

    f(x)=x4+x2+1.

  • Variant 4

    f(x)=x3+x.

Difficulty level: Easy task (using definitions and simple reasoning)
Proving or derivation task
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