Let F(R) be the vector space of all functions from R to R. Consider the functions v1, v2, v € F(R) defined by: v₁ = sin(x) + x e²x + 2x = e²x - 2 sin(x) Which of the following statement(s) is/are true? v₁, v2, v are linearly independent since Ov? + Ov? + Ov} = ♂. vi, v2, v are linearly dependent since Ov? + Ov? + Ovz = 0. v1, v2, v are linearly independent since 20 + 1v? − 1v3 = 0. v₁, v2, v3 are linearly dependent since -2v1 + 1v? − 1v} = Ơ. 000

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