psLinAlgebra2Qu - vectors. Is the conjecture true? Prove...

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Fall 2007 ARE211 Problem Set #07 Second Lin Algebra Problem Set Due date: Oct 23 Problem 1 What is the diference between a minimum spanning set For a vector space and a basis For a vector space. Provide an example highlighting this diference. Problem 2 Problem 3 Problem 4 Problem 5 Consider the Following conjecture: Let V be a vector space spanned by the set { v 1 , v 2 ,... v n } . The 1
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2 set { v 1 , v 2 ,... v n } is a minimal spanning set for V iF the vectors v 1 , v 2 ,... v n are linearly independent
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Unformatted text preview: vectors. Is the conjecture true? Prove your answer. Problem 6 Let U and W be vector subspaces of the vectorspace V. Dene the space U + W = { x | x = u + w , u U, w W } Show that U + W is a vector subspace of V. Problem 7 a) Let A be a symmetric (nxn) matrix with one or more negative eigenvalues. What can you say about the determinant of the matrix and its rank? b) Let A be symmetric (2x2) matrix. Is it true that A is indenite iF its determinant is negative. Explain your answer (No formal proof necessary)....
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This note was uploaded on 08/01/2008 for the course ARE 211 taught by Professor Simon during the Fall '07 term at University of California, Berkeley.

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psLinAlgebra2Qu - vectors. Is the conjecture true? Prove...

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