1.

1. (a) F

2. (b) T

3. (c) T

4. (d) F

5. (e) F

2. For $\text{W}=\text{span}(\{(1,2)\}),{[\text{T}]}_{\beta }=\left(\begin{array}{cc}{\displaystyle \frac{1}{5}}& {\displaystyle \frac{2}{5}}\\ {\displaystyle \frac{2}{5}}& {\displaystyle \frac{4}{5}}\end{array}\right).$

3. (2)

1. (a) ${\text{T}}_1(a,b)={\displaystyle \frac{1}{2}}(a+b,a+b){\text{ and T}}_2(a,b)={\displaystyle \frac{1}{2}}(a-b,-a+b)$

2. (d) $\begin{array}{l}{\text{T}}_1(a,b,c)={\displaystyle \frac{1}{3}}(2a-b-c,-a+2b-c,-a-b+2c)\text{ and }\\ {\text{T}}_2(a,b,c)={\displaystyle \frac{1}{3}}(a+b+c,a+b+c,a+b+c)\end{array}$