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 m3/min with a concentration of 10 mg/m and 1 m3/min with the concentration of vat 3, while the mixed and homogenous content of the vat is distributed at 3 m3/min to vat 5 and 3 m3/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 coi = 20 mg/m3 and Co3 = 10 mg/m