R$1=30,$ R$2=1\mathrm{.}8$k$,$ R$3=86,$ R$4=1\mathrm{.}5$M$,$ R$5=6\mathrm{.}8$k$,$ R$6=10$k$,$ R$7=3162\mathrm{.}3,$ R$8=50,$ R$9=3\mathrm{.}2$M$,$ R$10=10,$ V$1=163$V$,$ V$2=45$V$,$ V$3=54\mathrm{.}8$V

a$)$ Indicate the current direction for each loop.

b$)$ Write the loop equations and express the system of equations in matrix form.

c$)$ Solve the system of equations you created using Cramer's Rule.

d$)$ Show all elements of each matrix whose determinant you calculate.

i$)$ Do not attempt to calculate the determinants by hand. Use a program or online solvers. Simply write down the results you obtain. Do not round the determinants.

e$)$ Find the currents for each loop. If any currents have negative signs, redraw the circuit to show all currents in positive directions. $($Keep three decimal places after the comma, and be mindful of the units; avoid writing values like $0\mathrm{.}0000$xxx Amperes.$)$

f$)$ Calculate the voltages across the resistors according to the given polarity signs. $($The signs of the voltages you calculate are important. Keep three decimal places after the comma, and be mindful of the units; avoid writing values like $0\mathrm{.}0000$xxx Volts.$)$

g$)$ Calculate the power values necessary to prevent damage to the resistors, using a safety factor of $1\mathrm{.}5.$

h$)$ Calculate the power values necessary to prevent damage to the voltage sources, using a safety factor of $1\mathrm{.}5.$