e404k - MAS 3105 Quiz 4 Key Feb 25, 2004 Prof. S. Hudson 1)...

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MAS 3105 Feb 25, 2004 Quiz 4 Key Prof. S. Hudson 1) The matrix A is row equivalent to U (see below). Find a basis for N ( A ), and explain briefly how you know it is a basis. A = 1 3 0 9 4 1 1 4 19 2 1 1 2 11 2 U = 1 0 0 0 1 0 1 0 3 1 0 0 1 4 0 2) Which of the following sets S are subspaces of R 2 ? Explain each answer briefly. a) S = { ( x 1 ,x 2 ) T | 3 x 1 + 4 x 2 = 7 } b) S = { ( x 1 ,x 2 ) T | x 1 = x 2 } c) S = { ( x 1 ,x 2 ) T | x 1 = x 1 } d) S = { ( x 1 ,x 2 ) T | x 2 1 + x 2 2 = 0 } 3) Choose ONE of these to prove. You can answer on the back. a) If dim(V)= n > 0 and B = { v 1 ,v 2 ,...,v n } spans V then B is a basis of V. b) Show that a nonempty subset of a linearly independent set of vectors { v 1 ,v 2 ,...v n } is also linearly independent. c) Let L = { v 1 ,v 2 ,...,v n } be a spanning set of V and let v V be any other vector. Show that { v 1 ,v 2 ,...,v n ,v } is linearly dependent. Extra Credit (about 3-5 points): Should a Linear Algebra course include MATLAB in the
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e404k - MAS 3105 Quiz 4 Key Feb 25, 2004 Prof. S. Hudson 1)...

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