end the entire question through before beginning! The solution will need to be resented in stages in the different parts below. t a certain Community College, rst-year students in a particular program must take 100 level math class, a 100 level English class and a philosophy class. 1 order to satisfy this requirement in any given quarter, the college needs to make 8 ore sections of math classes available than sections of English classesj but only half as any sections of philosophy classes as sections of English classes. While planning for Fall quarter, it became clear that several factors (classroom avail- )ility, time of day, instructor availability) would limit the total number of sections of [ESE three courses to 63. ow many sections of each type of class should the college make available during fall latter? a) Write the problem as a system of three linear equations and three variables. WmW'L'll. - - ' - . - - - You may use general online resources to research how to answer an Exam question. - You may use an online or handheld graphing calculator, although you 3 2?? 01 $133 2.A=_ 3:31 0:0 0 D: 101 21 1V 401 200 " 210 Evaluate the following matrix expressions. If an expression cannot be evaluated, give a detailed reason. (21.) 2A3 3D (b) D(C + B) (c) Find A'1 . Solve the matrix equation Ax = b below by using an. inverse metres. Be sure to show the steps you tank to nd the inverse matrix. Briej,r describe what your answer means or what it represents. 0 3 2 HI] 1 4 2 I2 = 3 4 1 I3 MUG Solve the matrix equation AX = b below by the mechanical (not theoretical) technique of your choice. Notice that this is the same matrix equation as in question 2 with the exception of the vector b. Be sure to show the steps you take during any matrix multiplication. On this problem, you may use a calculator to do the matrix manipulation, but if you do, you must explain what you did on the calculator and why. Bonus: How could you have used the invertible matrix theorem to reach the same con- clusion? Be sure to include statements of any restrictions and how you know they are met. 0 3 2 $1 1 4 2 2:2 3 4 1 I3 || coo