Consider the following functions. f₁(x) = x, f₂(x) = x²,

Last updated: 7/8/2022

Consider the following functions. f₁(x) = x, f₂(x) = x², f3(x) = 5x - 4x² g(x) = c1f1(x) + c2f2(x) + c3f3(x) Solve for C1, C2, and C3 so that g(x) = 0 on the interval (-∞, ∞). If a nontrivial solution exists, state it. (If only the trivial solution exists, enter the trivial solution {0, 0, 0}.) {C1, C2, C3} Determine whether f1, f2, f3 are linearly independent on the interval (-∞, ∞). linearly dependent linearly independent