In C[0, 1], are the functions {x2 , x3 , e2x} linearly independent?

1. Show that y₁= ez and y2 = ze form a linearly independent set on the interval (-00,00).

3. In M3x2(F), prove that the set { ( ) ( ) ( ) ( ) ( ) } " 0 0 1 is linearly dependent.

Q2.1 have been given the following sets functions. Which of are linearly you them on the interval of (-∞0, ∞0) ? one right answer. more than independent There may be Leption f₁ (x) = x²₂ f₁₂ (x) = 3x²₂ f₂(x) = x² +6 option 2 f₁cx) = 3e³x₂f₂(x) = 9e⁹x - f₁₂(x) = 276²7x option 3 2 f₁(x) = 2sin ²³ x ₂ f₂(x) = 6 cos ²³ x 9 f₂(x)=x of