(a) 求使下列方程组没有唯一解的 $k$ 值：

(b) 已知 $k = 1$，证明第 (a) 部分的方程组相容，并从几何角度解释这一情形。

Answer all questions. You should use a calculator where appropriate.

You must show all necessary working clearly; no marks will be given for unsupported answers from a calculator.

Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.

请回答所有题目。适当时应使用计算器。必须清楚展示所有必要的计算过程；仅给出计算器答案而没有过程，不予评分。除非题目另有精度要求，非精确数值答案保留 3 位有效数字，以度为单位的角度保留 1 位小数。

系数矩阵的行列式为零时，方程组没有唯一解。沿第一行展开，再因式分解。

The system fails to have a unique solution exactly when the coefficient determinant vanishes. Expanding along the first row gives

Thus $\boxed{k=1\text{ or }k=4}$.

代入 $k=1$ 后，检查第三个方程是否由前两个推出。再让 $z$ 取任意值，写出公共解。

At $k=1$, eleven times the first equation minus four times the second gives the third, including its right-hand side $11-8=3$. Subtracting the first equation from the second gives $3y+3z=1$. Substituting into the first gives $x=\frac13-z$ as well. Therefore

The system is consistent, and the three planes intersect in this common line.