Given the vectors (a) Are x1, x2, x3, and x4 linearly independent in R3? Ex...

Given the vectors

(a) Are x₁, x₂, x₃, and x₄ linearly independent in R³? Explain.

(b) Do x₁, x₂ span R³? Explain.

(c) Do x₁, x₂, x₃ span R³? Are they linearly independent? Do they form a basis for R³? Explain.

(d) Do x₁, x₂, x₄ span R³? Are they linearly independent? Do they form a basis for R³? Explain or prove your answers.