1.

1. (a) F

2. (b) T

3. (c) F

4. (d) F

5. (e) T

6. (f) T

7. (g) T

2. The subspaces in (a), (c), and (d) are T-invariant.

6.

1. (a) $\left\{\left(\begin{array}{l}1\\ 0\\ 0\\ 0\end{array}\right),\left(\begin{array}{l}1\\ 0\\ 1\\ 1\end{array}\right),\left(\begin{array}{r}1\\ -1\\ 2\\ 2\end{array}\right)\right\}$

2. (c) $\left\{\left(\begin{array}{cc}0& 1\\ 1& 0\end{array}\right)\right\}$

9.

1. (a) $-t(t^2-3t+3)$

2. (c) $1-t$

10.

1. (a) $t(t-1)(t^2-3t+3)$

2. (c) ${(t-1)}^3(t+1)$

18.

1. (c) $A^{-1}={\displaystyle \frac{1}{2}}\left(\begin{array}{rrr}2& -2& -4\\ 0& 1& 3\\ 0& 0& -2\end{array}\right)$

31.

1. (a) $t^2-6t+6$

2. (c) $-(t+1)(t^2-6t+6)$