MAT 211 EXAM 2 REVIEW - ORDINARY DIFFERENTIAL EQUATIONS...

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MAT 211 Exam 2 Review 1) Solve the following systems. a) 3x – 2y = 9 b) 5x + 2y = 0 c) 4x + 2y = 9 d) 3x + y = A 4y = 6x – 18 3x + 8y = 17 y = 4 – 2x 2x + 2y = B 2) The solutions to a system of linear equations are as follows; (4z + 5, z – 3, z) for any real number z. a) Find the solution in terms of x b) Find the solution in terms of y 3) Mark is making a solution out of two different chemicals. Chemical A costs $3.20 per ounce and chemical B costs $4.80 per ounce. He makes 20 ounces of solution and it costs him a total of $82.80. How much of each chemical did he use? 4) Use Gauss-Jordan elimination (basic row operations to put the following matrix in Reduced Row Echelon Form. List the operations. 18 5 3 1 0 1 2 0 19 2 3 4 5) Write the system in matrix form AX = B, where A, B, and X are all matrices. 2x – 3y = 5 x + y + z = 4 x – 2y – 4z = -13 Then solve the system using an inverse matrix. 6) Using the matrices to the left and assuming that the variables are x, y, and z, respectively, write the solutions on the right. If necessary, leave the LEFTMOST variables arbitrary where applicable (start with x if necessary, then y if necessary). a) 0 0 0 0 5 0 1 0 3 1 0 1 b) 1 0 0 0 2 0 1 0 3 0 0 1 c) 1 1 0 0 2 0 1 0 3 0 0 1 d) 0 0 0 0 0 0 0 0 3 3 2 1 7) Let A = 2 4 0 3 and B = 4 2 2 1 . Find the following. a) 2B b) 2A – B c) 3AB – A 8) Use the following matrices to answer below.
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