Linear Algebra - Linear Independence / Dependence

Question

Determine whether the polynomials,

p1 = 1 - x , p2 = 5 + 3x - 2(x^2) , p3 = 1 + 3x - (x^2)

are linearly dependent or linearly independent in P2.

Answer 1

Form a matrix from vectors of the coefficients x⁰, x¹ and x²

[ 1 5 1]

[-1 3 3]

[0 -2 -1]

The determinant of this matrix is zero, so the polynomials are dependent.