Given the system of equations−3x2+7x3=2,x1+2x2–x3=3,5x1 −2x2=2(a). Compute the determinant. (b). Use Cramer’s rule to solve for the x’s. (c). Use Gauss elimination with partial pivoting to solve for the x’s. (d). Substitute your results back into the original equations to check your solution.

Air enters a horizontal, constant-diameter heating duct operating at steady state at 290 k, 1 bar, with a volumetric flow rate of 0.25 m°/s, and exits at 325 k, 0.95 bar. the flow area is 0.04 m2. assuming the ideal gas model with k = 1.4 for the air, determine (a) the velocity at the inlet and exit, each in m/s, and (c) the rate of heat transfer, in kw flow rate, in kg/s, (b) the mass kg 0.3