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pset2

# pset2 - Physics(PHZ 3113 Mathematical Physics Florida...

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Physics (PHZ) 3113 Mathematical Physics Florida Atlantic University Fall, 2010 Problem Set II Due: Tuesday, 7 September 2010 1. (Problem 3.8.4, p. 136) Determine whether the vectors 3 5 - 1 , 1 4 2 , - 1 0 5 and 6 14 5 are linearly dependent or independent. If they are linearly dependent, ﬁnd a maximal linearly independent subset and write each of the given vectors as a linear combination of those linearly independent ones. 2. (Problems 3.8.17 and 27, pp. 136–137) a. Solve the following system of homogeneous linear equations by row reducing the matrix: x - 2 y + 3 z = 0 x + 4 y - 6 z = 0 2 x + 2 y - 3 z = 0 b. Solve the following system of inhomogeneous linear equations and write the solution in vector form, as in (8.11) and (8.13) in the book: x - y + 2 z = 3 - 2 x + 2 y - z = 0 4 x - 4 y + 5 z = 6 3. (Problems 3.9.8 and 18, pp. 141–142) a. Prove that ( AB ) = B A for all matrices A and B (whose product exists). Hint

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pset2 - Physics(PHZ 3113 Mathematical Physics Florida...

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