# a3 - 2 a 2 Does V with these operations form a vector space...

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ASSIGNMENT 3 EE441 KUMAR Fall 2007 Due: Sep. 21 1. Factor the symmetric matrix A = " 13 10 10 8 # . into a product A = SS T (Cholesky decomposition), where S is a lower triangular matrix. 2. Is the matrix A = 1 - 2 1 0 6 - 3 16 - 4 2 4 7 - 2 3 - 6 6 2 singular ? Show all your working. 3. Use the Gauss-Jordan method to ﬁnd the inverse of the matrix A = 0 - 1 1 2 1 4 5 3 9 4. Consider the set V = < 2 with addition deﬁned by [ x, y ] [ w, z ] = [ x + w + 1 , y + z - 2] and scalar multiplication ± deﬁned by a ± [ x, y ] = [ ax + a - 1 , ay -
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Unformatted text preview: 2 a + 2] . Does V with these operations, form a vector space ? If your answer is yes, identify the identity element and the additive inverse of each element. If your answer is no, explain clearly, why you feel this fails to be a vector space. Start by stating all the axioms that deﬁne a vector space and your conclusions on each of the axioms. (CARE – Do not jump to conclusions on this problem). 1...
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