Problem 1 (paper) Use Gauss-Jordan elimination with partial pivoting to solve the following linear system. Show all steps. Represent all values as exact fractions, not decimal numbers. [2 1 1 4 2 1 3 1 1] [x1 x2 x3] = [8 13 10]
Problem 2 (paper) For the matrix-matrix
A = [2 3 2 4 7 6 6 11 13]
Calculate the LU decomposition A = LU where
L = [1 0 0 l21 1 0 l31 l32 1] and U = [u11 u12 u13 0 u22 u23 0 0 u33]
As follows. Mulitply out LU to get algebraic expressions for each component of A in terms of the components of L and U.

Amass of m 1.5 kg of steam is contained in a closed rigid container. initially the pressure and temperature of the steam are: p 1.5 mpa and t 240°c (superheated state), respectively. then the temperature drops to t2= 100°c as the result of heat transfer to the surroundings. determine: a) quality of the steam at the end of the process, b) heat transfer with the surroundings. for: p1.5 mpa and t 240°c: enthalpy of superheated vapour is 2900 kj/kg, specific volume of superheated vapour is 0. 1483 m/kg, while for t 100°c: enthalpy of saturated liquid water is 419kj/kg, specific volume of saturated liquid water is 0.001043m/kg, enthalpy of saturated vapour is 2676 kj/kg, specific volume of saturated vapour is 1.672 m/kg and pressure is 0.1 mpa.

Calculate the bore of a cylinder that has a stroke of 18 inches and an extension time of 6 seconds at a flow rate of 4 gal/min.

Agas mixture consists of 8 kmol of h2 and 2 kmol of n2. determine the mass of each gas and the apparent gas constant of the mixture.