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1. Solve the linear system using Gaussian elimination on augmented matrix and compute A-1. 212 + =7 201 I2 + 4x3 = 17 301 212 + = 14 2. Write the solution set for each system in parametric vector form. Identify in each case the homogeneous solution TH and the particular solution Ip (a) 2x1 - 512 + 13 - 2 (b) X1 + 12 + 213 - 15 = 4 X4 + 215 - 3 3. Given the objective function z - I1 - 212 find the maximum and minimum values of z + 212 4 subject to: + 2 3 and: x1 2 0, 12 2 0. (a) Sketch the feasible region in the 2172 plane. Label the coordinates of all corner points. (b) Find the maximum and minimum points and values of z. (c) Write the minimization problem in standard form. Then state the dual maximum program. (d) Solve the problem again using the simplex method. After each pivot step, label the basic variables and write the corresponding vertex. 4. Given the linear program: Maximize: 2 = 321 + 212 - 13 12 13 subject to: 212 312 213 -5 and: 21 2 0,22 _ 0, 23 2 0. (a) Write the dual linear program. ImagineBook