We start with functions y₁= 5x and y₂ = 2x²+3x. First, explain to me why the set {y₁, y2, Y3} where y3 = x²-3x is a linearly

Question

We start with functions y₁= 5x and y₂ = 2x²+3x. First, explain to me why the set {y₁, y2, Y3} where y3 = x²-3x is a linearly dependent set. Second, give me an example of a function y4 in the space so that {y₁, y2, Y4} is linearly independent.

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