b) Let \( S=\left\{v_{1}, v_{2}, v_{3}\right\} \) be a linearly independent set of the vectors in \( \mathbb{R}^{n} \) and \( T=1 \) \( \left\{u_{1}, u_{2}, u_{3}\right\} \). Prove that \( T \) is linearly independent set. where \( u_{1}=v_{1}+v_{2}+v_{3}, u_{2}=v_{2}+v_{3} \), and \( u_{3}=v_{3} \).

1. Calcula dos números cuya suma sea 100 y de forma que su producto sea máximo.

Determine the solution set of the following. \( \begin{array}{ll}\text { 1. }-3 x+4=-1 & \text { 6. } \frac{13+2 x}{4 x+1}=\frac{3}{4} \\ \begin{array}{ll}\text { 2. } 4 x-3=-5 x+6 & \text { 7. } 8-\frac{5}{x}=2+\frac{3}{x} \\ \text { 3. } 4(2 y+5)=3(5 y-2) & \text { 8. }(3 x-2)^{2}=(x-5)(9 x+4) \\ \text { 4. } 6(2 y+3)-3(y-5)=0 & \text { 9. }(5 x-7)(2 x+1)-10 x(x-4)=0 \\ \text { 5. } \frac{3+5 x}{5}=\frac{4-x}{7} & \text { 10. } \frac{-5}{3 x-9}+\frac{4}{x-3}=\frac{5}{6}\end{array}\end{array} \$ \begin{array}{l}\end{array} \)

Show all your work for each problem. You may earn partial credit on each problem/pro use your note guides from these sections and a calculator. 1) a. Find the inverse function of \( g . \quad g(x)=3+\sqrt{7+x} \)

7. \( \frac{3}{4}(2 x+1)=\frac{2}{3}(x+1) \)

\( \frac{a}{x+a}+\frac{b}{x-b}=\frac{a+b}{x-c} \)