Problem 3: Communication Network Problems [40 total points]. (i) Use graph theory and linear algebra (e.g., introduction to connected systems we discussed at the beginning of the course.) to sketch a connected three multi-agent system and label the systems 1-3. [2 points] (ii) Use linear algebra, such as matrices and vectors to describe the connected systems in (i). [3 points] (iii) Use linear algebra such as matrices, vectors, matrix multiplications, and bit-wise operations where system 1 received data from systems 2 and 3 to authenticate connection establishment for communication (e.g., matrix equation: Ax=b, for matrix multiplication use exclusive or for addition) to describe the connected systems in (i). [15 points] (iv) Describe the difference between trusted vs untrusted systems. [2 points] (v) Assume the trusted system 1 is attacked by receiving arbitrary false injections to disrupt connection from untrusted systems 2 and 3. Use linear algebra similar to (iii) to describe the adversarial effect on system 1. [15 points] (vi) Sketch an example of system-to-system communication using virtualization tools. Provide examples of mitigation systems to secure system information over transmission lines. [3 points]