The system of mixing tanks shown in Figure 8.2.7 is a closed system. The tanks A, B, and C initially contain the number of gallons of brine indicated in the figure. Figure 8.2.7 Mixing tanks mixture 5...

Solve the exercise in the image, by using differential equations, solve the 3 sections, that is, a, b and c, without omitting any step to arrive at the result.

Extracted text: The system of mixing tanks shown in Figure 8.2.7 is a closed system. The tanks A, B, and C initially contain the number of gallons of brine indicated in the figure. Figure 8.2.7 Mixing tanks mixture 5 gal/min A B C 100 gal 100 gal 50 gal mixture mixture 5 gal/min 5 gal/min (a) Construct a mathematical model in the form of a linear system of first- order differential equations for the number of pounds of salt ¤1 (t), x2(t) and æ3 (t) in the tanks A, B, and C at time t, respectively. Write the system in matrix form. (b) Use the eigenvalue method of this section to solve the linear system in part (a) subject to x1(0) = 30, x2(0) = 20, x3(0) = 5.