Chapter 4.1, Problem 6E

Determine whether the following are linear transformations from ${ℝ}^2$ into ${ℝ}^3$ .
(a) $L(x)={(x_1,x_2,1)}^T$
(b) $L(x)={(x_1,x_2,x_1+2x_2)}^T$
(c) $L(x)={(x_1,0,0)}^T$
(d) $L(x)={(x_1,x_2{x}_1^2+x_2^2)}^T$