Question

\text { Given the linear transformation } T: \mathbb{R}^{3} \rightarrow \mathbb{R}^{3}, \text { such that } T(\vec{x})=A \vec{x}, \text { where } A= \left[\begin{array}{ccc} 3 & 2 & 4 \\

2 & 1 & 3 \\ 5 & -4 & 14 \end{array}\right] find the Kernel and the Range of T.

Fig: 1

Fig: 2

Fig: 3