The figure shows a network with 8 edges. Any flow is positive from the node i...

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The figure shows a network with 8 edges. Any flow is positive from the node i to node j when i < j, as usual. The figure is also representative of a truss with 8 bars. The lowest two nodes are grounded in the network (x = x7 = 0) and they are supported as pin joints in the truss. The upper 5 nodes are free and the edges are num- bered. (a) Find the incidence matrix A for the grounded network. (b) What are all solutions to Ax=0? (c) How many independent solutions are there to A y=0? 1 1 2 45 2 3 3 4 5 60 4 5 7 8 6. 7 (d) If 1 amp enters node 1 and travels to ground, what equations would you solve for the potentials x and currents y? Assume all c;= 1. grounded/supported (e) What are the 8 currents? (You can answer from the picture without solving equations). (f) What is the shape of the matrix A for the truss problem associated with the figure? (g) What are the mechanisms (solutions to Ax = 0 for this truss? Describe them briefly and also provide the solutions in the usual order, that is x=(x,y,...). Also, let positive in the horizontal direction be to the right. Let positive in the vertical direction be down. (h) For the truss stiffness matrix K-ATA, is K positive definite or positive semidefinite? Explain your reasoning. (i) Find a set of horizontal and vertical forces f, not all zero, so that Kx=f can be solved. The figure shows a network with 8 edges. Any flow is positive from the node i to node j when i < j, as usual. The figure is also representative of a truss with 8 bars. The lowest two nodes are grounded in the network (x = x7 = 0) and they are supported as pin joints in the truss. The upper 5 nodes are free and the edges are num- bered. (a) Find the incidence matrix A for the grounded network. (b) What are all solutions to Ax=0? (c) How many independent solutions are there to A y=0? 1 1 2 45 2 3 3 4 5 60 4 5 7 8 6. 7 (d) If 1 amp enters node 1 and travels to ground, what equations would you solve for the potentials x and currents y? Assume all c;= 1. grounded/supported (e) What are the 8 currents? (You can answer from the picture without solving equations). (f) What is the shape of the matrix A for the truss problem associated with the figure? (g) What are the mechanisms (solutions to Ax = 0 for this truss? Describe them briefly and also provide the solutions in the usual order, that is x=(x,y,...). Also, let positive in the horizontal direction be to the right. Let positive in the vertical direction be down. (h) For the truss stiffness matrix K-ATA, is K positive definite or positive semidefinite? Explain your reasoning. (i) Find a set of horizontal and vertical forces f, not all zero, so that Kx=f can be solved.