In the vector space P_4 of all polynomials of degree less than or equal to 4 we define the first five Tchebychev polynomial as(adsbygoogle = window.adsbygoogle || []).push({});

p_0(x) = 1

p_1(x) = x

p_2(x) = 2x^2 - 1

p_3(x) = 4x^3 - 3x

p_4(x) = 8x^4 - 8x^2 + 1

To show that B={p_0, p_1, p_2, p_3, p_4} is a basis of P_4, do I put them in a matrix, find the row-echelon form and find the vector space with pivots? I so, how do I put it in a matrix?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Vector Space: Basis

**Physics Forums | Science Articles, Homework Help, Discussion**