Independence of functions

Task number: 2521

Decide, whether the following sets of vectors are linearly independent in the space of real functions \(\mathbb R\to\mathbb R\) (over the field \(\mathbb R\)).

  • Variant 1

    \(\{2x-1,x-2, 3x\}\).

  • Variant 2

    \(\{x^2+2x+3, x+1, x-1\}\).

  • Variant 3

    \(\{\sin(x), \cos(x)\}\).

  • Variant 4

    \(\{\sin(x+1), \sin(x+2)\, \sin(x+3)\}\).

  • Variant 5


    (i.e. the natural, decadic and binary logarithm.)

Difficulty level: Moderate task
Proving or derivation task
Cs translation
Send comment on task by email