Enter the matrix a and the vector b in matlab: a = [4 1 2 −3; −3 3 −1 4; −1 2 5 1; 5 4 3 −1] , b = [−16; 20; −4; −10]the exact solution to the system ax = b is the vector x = (−1, 1, −2, 3)^t .(a) enter [l, u,p] = lu(a) to find the lu decomposition of the matrix p a (don’t forget that you will need p*b). verify that p a = lu.(b) use the lu decomposition you found in part (a) to solve the system ax = b. call the computed solution x_lu.(c) enter the vector x and compare your solution x lu from part (b) with the exact solution x by computing norm(x_lu - x)

An air conditioning system consist of a 5 cm diameter pipe, operating at a pressure of 200 kpa. the air initially enters the pipe at 15°c with a velocity of 20 m/s and relative humidity of 80%. if the heat supply throughout the process is 960 w, determine the relative humidity and the temperature at the outlet

Ahe-xe mixture containing a 0.75 mole fraction of helium is used for cooling electronics in an avionics application. at a temperature of 300 k and atmospheric pressure, calculate the mass fraction of helium and the mass density, molar concentration and molecular weight of the mixture. if the cooling capacity is 10 l, what is the mass of the coolant?

Along 8-cm diameter steam pipe whose external surface temperature is 900c connects two buildings. the pipe is exposed to ambient air at 70c with a wind speed of 50 km/hr blowing across the pipe. determine the heat loss from the pipe per unit length. (b) air at 500c enters a section of a rectangular duct (15 cm x 20 cm) at an average velocity of 7 m/s. if the walls of the duct are maintained at 100c. a) the length of the tube for an exit temperature of the air to be 40 0c. b)the rate of heat transfer from the air. c) the fan power needed to overcome the pressure drop in this section of the duct.