A The function $f(x)=e^{\frac{x}{2}}-2x$ has a root on $0$;$2.$ Find the root using

a$)$ Bisection method.

b$)$ False position method.

Write "Matlab" codes to solve the question. Use four significant figures. End the program after approximate relative error is below $0\mathrm{.}01\%.$

Add your codes to your solution. Explain which method finds the solution faster.

Use Naive Gauss Elimination to solve the following equation system.

$8x_1+2x_2-2x_3=-2$

$10x_1+2x_2+4x_3=4$

$12x_1+2x_2+2x_3=6$

Write "Matlab" codes to solve the question. Use four significant figures. Don't forget to check if the system is ill conditioned. Check if the system requires pivoting.

Add your codes to your solution. Does the system have unique solution? Explain.