Question: Hi, need linear algebra help with these problems please 1. For the complete graph with 4 nodes and all 6 possible edges: (a) Write down

Hi, need linear algebra help with these problems please

1. For the "complete graph" with 4 nodes and all 6 possible edges: (a) Write down the incidence matrix A. (b) What is the rank of A and A = CR factorization? (c) What is the dimension of the left nullspace N(AT)? (d) Find a full set of solutions to Kirchhoff's Current Law ATy = 0 2. Proof question in linear algebra: Why does nullspace of AT A = nullspace of A? (a) If x is in N(A) check that r is in N(ATA). (b) If x is in N(AT A) why is x] AT Ax - 0? This means that || Ax| |2 = 0. Therefore x is in N(A). (c) How do we also know that rank (ATA) = rank (A)? 3. Show that rank (A + B)

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