Chapter 2.1, Problem 2E

GOAL Use the concept of a linear transformation in terms of the formula $\stackrel{\to }{y}=A\stackrel{\to }{x}$, and interpret simple linear transformations geometrically Find the inverse of a linear transformation from ${ℝ}^2$to ${ℝ}^2$(if it exists). Find the matrix of a linear transformation column by column.

Consider the transformations from ${ℝ}^3$to ${ℝ}^3$defined in Exercises 1 through 3. Which of these transformations are linear?

2. $\begin{array}{l}{y}_1=2x_2\\ y_2=3x_3\\ y_3=x_1\end{array}$