In column vectors are written as rows such as x x1 x2 and

Question

Question: In column vectors are written as rows, such as x = (x₁, x₂), and T (x) is written as T (x₁, x₂).

Let T : R³ → R³ be the transformation that reflects each vector x = (x₁, x₂, x₃) through the plane x3 = 0 onto T (x) = (x₁, x₂, x₃). Show that T is a linear transformation.