A. (5 pts) find the determinant of a by row reduction to ref and then using the determinant properties (no expansion is required). what properties did you use? you must ensure that the properties you use does not change the value of the determinant. show your work. b. (2 pts) what is the determinant of (2�: ) ? c. (2 pts) what is the determinant of 2�; $ ? d. (2 pts) what is the determinant of 2� ; $ ?

Air is to be cooled in the evaporator section of a refrigerator by passing it over a bank of 0.8-cm-outer-diameter and 0.4-m-long tubes inside which the refrigerant is evaporating at -20°c. air approaches the tube bank in the normal direction at 0°c and 1 atm with a mean velocity of 4 m/s. the tubes are arranged in-line with longitudinal and transverse pitches of sl- st 1.5 cm. there are 30 rows in the flow direction with 15 tubes in each row. determine (a) the refrigeration capacity of this system and (b) pressure drop across the tube bank. evaluate the air properties at an assumed mean temperature of -5°c and 1 atm. is this a good assumption?