Consider the setup of chemical vats illustrated in the Figure below. In each vat, a volume of chemical mix with a certain concentration enters, is mixed until it becomes homogenous, and then is distributed to other vats. For example, in vat 1. the input is 5 m/min with a concentration of 10 mg/m2 and 1 m/min with the concentration of vat 3. while the mixed and homogenous content of the vat is distributed at 3 m/min to vat 5 and 3 m/min to vat 2. a) Use LU factorization to determine the concentrations of the two outputs of the system. b) Also, solve the system when the input concentrations to vat 1 and vat 3 are changed to co1 = 20 mg/m' and co3 = 10 mg/m. V50 = 3 V13 = 3 Vat 5 Vs4 = 2 V25 = 2 Voi = 5 Col = 10 V12= 3 V42 = 1 V40 = 10 Vat 1 Vat 2 Vat 4 V23 = 2 V31 = 1 V34 = 9 Vat 3 Vo3 = 8 CO3 = 20 Show transcribed image text