Given a scalar r, define T : \mathbb{R} ^{2}\rightarrow \mathbb{R} ^{2} by T(x) = rx. T is called a contraction when 0 ≤ r ≤ 1 and a dilation when r > 1. Let r = 3, and show that T is a linear transformation.
Given a scalar r, define T : \mathbb{R} ^{2}\rightarrow \mathbb{R} ^{2} by T(x) = rx. T is called a contraction when 0 ≤ r ≤ 1 and a dilation when r > 1. Let r = 3, and show that T is a linear transformation.