3. (20%) Let L(x) = (x₁ + x₂, x₂ - x₃)ᵀ be the transformation from ℝ³ to ℝ².
(a) Determine whether L is a linear transformation.(b) Determine the standard matrix representation A and find L(x) for x = [1, 2, 3]ᵀ.
3. (20%) Let L(x) = (x₁ + x₂, x₂ - x₃)ᵀ be the transformation from ℝ³ to ℝ².
(a) Determine whether L is a linear transformation.(b) Determine the standard matrix representation A and find L(x) for x = [1, 2, 3]ᵀ.