10/21 作业

1. (a) $\left\{ (a + b, a + 2b, a + 3b, a + 4b) \in \R^4 \mid a, b \in \R \right\}$ .

   (b)

   (1) $\left\{ (a, b, c) \in \R^3 \mid a + 2b + 3c = 0,\, a, b, c \in \R \right\}$ .

   (2) $\left\{ (a, -2a, a, 0) \in \R^4 \mid a \in \R \right\}$ .

2. $\left\{ \mathbf v \in \R^3 \mid v = (0, -\frac{3}{4}, -\frac{5}{4}) + a (1, -\frac{3}{4}, -\frac{5}{4}),\,a \in \R \right\}$ .

3. (a) Yes.

   (b) No.

   (c) No.

   (d) Yes.

   (e) Yes.

   (f) Yes.

   (g) No.

   (h) Yes.

4. (a) False.

   (b) True.

   (c) True.

   (d) False.