計算機數學

(4分) How many of the following statements are True?

(1) Suppose that $T: \mathbb{R}^2 \to \mathbb{R}^3$ is linear and $T(1,2) = (1,0,2)$ and $T(2,3) = (1,-1,4)$. Is $\mathrm{Ker}(T) = \{0\}$?

(2) The linear transformation $L: P_2 \to P_2$ defined by $L(at^2+bt+c) = 2a+b$ is one to one.

(3) Suppose that $T: \mathbb{R}^2 \to \mathbb{R}^3$ is defined by $T\left(\begin{bmatrix}x_1\\x_2\end{bmatrix}\right) = \begin{bmatrix}2x_1-x_2\\-x_1\\6x_1\end{bmatrix}$. Is $T$ onto?