申論題

14.  Let matrix $A \in \mathbb{R}^{3 \times 4}$ have its $A_{ref} = \begin{bmatrix} 1 & 1 & 2 & 0 \\ 0 & 1 & -2 & -1 \\ 0 & 0 & 0 & 0 \end{bmatrix}$. 

 (b) Let $\mathbf{z} = \begin{bmatrix} 1 \\ 2 \\ y \end{bmatrix} \in R(A)$. Find all possible values of $y$ such that the distance (in 2-norm) between $\mathbf{z}$ and $N(A)$ is $\sqrt{6}$.