Find an example of 4 linearly independent vectors a₁, a₂, a₃, a₄ ∈ R 4 such that the linear transformation T : R 4 → R 4 , T(x) = x₁a₁ + x₂a₂ + x₃a₃ + x₄a₄ is not onto, OR explain why this is not possible. If you provide an example, your answer should include an explanation of why those vectors have the desired properties.

Find a parametrization for the curve「and determine the work done on a particle moving along γ in r3 through the force field f: r^3--r^3'where f(x, y,z) = (1,-x, z) and (a) im (γ) is the line segment from (0,0,0) to (1,2,1) (b) im (γ) is the polygonal curve with successive vertices (1,0,0), (0,1,1), and (2,2,2) (c) im (γ) is the unit circle in the plane z = 1 with center (0,0,1) beginning and ending at (1,0,1), and starting towards (0,1,1)