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MATH_215_Test2

# MATH_215_Test2 - Practice Test 2 For full credit show all...

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Practice Test 2 For full credit, show all work. 1 State the definition for the following: a) A basis for a subspace S . b) An invertible matrix M . c) rank( A ). 2 Given A = 3 1 4 6 2 0 1 3 - 1 1 2 0 . Find the following: a) A basis for null( A ). b) A basis for column( A ). 3a) Show that projection onto y = 2 x is a linear transformation. b) Find the standard matrix representation for the projection. 4 Find counter-examples to the following false statements: (10 pts each) a) ( A + B ) - 1 = A - 1 + B - 1 . b) AB = AC = B = C . 5a) Find the LU factorization for A = 2 1 - 2 - 2 3 - 4 4 - 3 0 . b) Use the LU factorization to solve the sytem A x = - 3 1 0 . 6 Suppose the weather of a city is a Markov process. The probability that tomorrow is dry is 8/10 if today is dry, and 4/10 if today is wet.

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MATH_215_Test2 - Practice Test 2 For full credit show all...

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