1.

1. (a) F

2. (b) T

3. (c) T

4. (d) T

5. (e) F

6. (f) T

7. (g) T

2.

1. (a) $\left(\begin{array}{r}4\\ -3\\ -1\end{array}\right)$

2. (c) $\left(\begin{array}{r}2\\ 3\\ -2\\ -1\end{array}\right)$

3. (e) $\left\{\left(\begin{array}{r}4\\ 0\\ 1\\ 0\end{array}\right)+r\left(\begin{array}{r}4\\ 1\\ 0\\ 0\end{array}\right)+s\left(\begin{array}{r}1\\ 0\\ 2\\ 1\end{array}\right)\text{: }r,s\in R\right\}$

4. (g) $\left\{\left(\begin{array}{r}-23\\ 0\\ 7\\ 9\\ 0\end{array}\right)+r\left(\begin{array}{r}1\\ 1\\ 0\\ 0\\ 0\end{array}\right)+s\left(\begin{array}{r}-23\\ 0\\ 6\\ 9\\ 1\end{array}\right)\text{: }r,s\in R\right\}$

5. (i) $\left\{\left(\begin{array}{r}2\\ 0\\ 0\\ -1\\ 0\end{array}\right)+r\left(\begin{array}{r}0\\ 2\\ 1\\ 0\\ 0\end{array}\right)+s\left(\begin{array}{r}1\\ -4\\ 0\\ -2\\ 1\end{array}\right)\text{: }r,s\in R\right\}$

4.

1. (a) $\left\{\left(\begin{array}{r}{\displaystyle \frac{4}{3}}\\ {\displaystyle \frac{1}{3}}\\ 0\\ 0\end{array}\right)+t\left(\begin{array}{r}1\\ -1\\ 1\\ 2\end{array}\right)\text{: }t\in R\right\}$

2. (c) There are no solutions.

5. $\left(\begin{array}{rrrrr}1& 0& 2& 1& 4\\ -1& -1& 3& -2& -7\\ 3& 1& 1& 0& -9\end{array}\right)$

7. $\{u_1,u_2,u_5\}$

11.

1. (b) $\{(1,2,1,0,0),(2,1,0,0,0),(1,0,0,1,0),(-2,0,0,0,1)\}$

13.

1. (b) $\{(1,0,1,1,1,0),(0,2,1,1,0,0),(1,1,1,0,0,0),(-3,-2,0,0,0,1)\}$