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Monthly Archives: September 2012
Linear Algebra and Its Applications, Exercise 2.5.3
Exercise 2.5.3. Given the incidence matrix from exercise 2.5.1 and any vector in the row space of show that . Prove the same result based on the linear system . What is the implication if , , and are currents … Continue reading
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Linear Algebra and Its Applications, Exercise 2.5.2
Exercise 2.5.2. Given the incidence matrix from exercise 2.5.1 and any vector in the column space of show that . Prove the same result based on the rows of . What is the implication for the potential differences around a … Continue reading
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Linear Algebra and Its Applications, Exercise 2.5.1
Exercise 2.5.1. Describe the incidence matrix for the following graph: The graph has three nodes and three edges, with edge 1 going from node 2 to node 1, edge 2 going from node 3 to node 2, and edge 3 … Continue reading
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Linear Algebra and Its Applications, Exercise 2.4.21
Exercise 2.4.21. Suppose that for two matrices and the associated subspaces (column space, row space, null space, and left nullspace) are the same. Does this imply that ? Answer: The answer is no, as shown by the following counterexample: We … Continue reading
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