Consider the single-input single-output LTI system x_ = 2 4 1 1 1 0 1 1 0 0 1 3 5 | {z } T 2 4 1 1 0 0 1 0 0 0 1 3 5 2 4 1 1 0 0 1 1 0 0 1 3 5 | {z } T1 x + 2 4 b1 b2 b3 3 5u: What conditions should b1; b2; b3 satisfy for the system to be controllable? You will need to simplify the conditions to the simplest possible form to get the full credit. 4

Graph the system of inequalities presented here on your own paper, then use your graph to answer the following questions: y > 2x + 3y is less than negative 3 over 2 times x minus 4part a: describe the graph of the system, including shading and the types of lines graphed. provide a description of the solution area. (6 points)part b: is the point (â’4, 6) included in the solution area for the system? justify your answer mathematically. (4 points)