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Consider the arc incidence matrix E of a graph. This matrix has a row for each node and a column for each arc. The component corresponding to the ith row and a given arc is a 1 if the arc is outgoing from i, is a -1 if the arc is incoming to i, and is a 0 otherwise. Show that E is totally unimodular (cf. the discussion in Section 5.5). Hint: We must show that the determinant of each square sub matrix of E is 0, 1, or -1. Complete the details of the following argument, which uses induction on the dimension of the sub matrix. The sub matrices of dimension 1 of E are the scalar components of E, which are 0, 1, or -1. Suppose that the determinant of each square sub matrix of dimension n ≥ 1 is 0, 1, or -1. Consider a square sub matrix of dimension n + 1. If this matrix has a column with all components 0, the matrix is singular, and its determinant is 0. If the matrix has a column with a single nonzero component (a 1 or a -1), by expanding its determinant along that component and using the induction hypothesis, we see that the determinant is 0, 1, or -1. Finally, if each column of the matrix has two components (a 1 and a -1), the sum of its rows is 0, so the matrix is singular, and its determinant is 0.
Discuss the advantages and disadvantages of outsourcing IT.
If the piston is moving downwards, and the coefficient of static friction at the contact points is µs = 0.2, determine the radius of the friction circle at each connection.
Compare and contrast the 3 selected frameworks
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How would you solve the following in C++? Please write code below: Write a condition-controlled while loop that allows the user to enter the calories they burned.
When is inflation an important issue in conducting an analysis and creating a business plan? Why bother?
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Thus, this dictionary needs frequent retrievals and occasional insertions. Which implementation of the ADT dictionary would be most efficient as a spell checker's dictionary?
The ystem is using a 2x1 multiplexer (0.6ns delay) and k-bit tag comparator (k/10ns delay).Let H1 denotes hit latency for 2-way set associative cache and H2 denotes hit latency for direct mapped cache. What will be the values of H1 and H2.
List at least six (6) main business and technical issues (and any other issues) that CFCL would need to consider in determining its business strategy (i.e. At least 12 issues in all).
If µs = 0.2 for the threads, and the torque applied to the handle is 1.5 N , determine the compressive force F on the block.
Evaluate following integrals using simpson's rule and corrected simpson's rule (or richardson extrapolation in case the corrected simpson's is not applicable). In each case, use n = 2,4,8,16,32.
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