SampleFinal

SampleFinal - , based on the basis found. a) = , = + + : ,...

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Math121A Sample Final Exam WQ10 1 Name: Signature: Instructions: 1. Check that you have pages 1 through 5 and that none are blank. 2. Do not spend too much time on a particular problem. Work the easier problems first. 3. The grading of this exam is based on your method. Show all of your work. If you need additional space, use the backs of the exam pages. 1) Determine whether the following vectors are linearly independent in g G (ℝ) . Show your work. {3± G G − 10± + 15,10± − 15} 2) Let ² = ³ 1 8 3 x y z −3 7 2 ´ . Given det(²) = 5 , computer the determinant of the following matrix. µ = ¶ ± · ¸ 1 8 3 −9 21 6 ¹
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Math121A Sample Final Exam WQ10 2 3) Consider the following subspace of g : G = ±²³´ µ¶ 1 2 1 3 ·, ¶ 3 6 3 9 ·, ¶ 1 3 5 4 ·, ¶ 2 3 −2 5 ·¸ Find a basis for G . 4) Find A ¹º given A = » 1 1 1 1 0 0 0 1 2 ¼ .
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Math121A Sample Final Exam WQ10 3 5) Given A = g 1 3 5 2 4 6 1 2 3 9 7 4 G , find a basis for Nul( A ). 6) Find a basis for each of the following subspace ± of the given vector space ² . Construct an isomorphism from ± to ³ for some
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Unformatted text preview: , based on the basis found. a) = , = + + : , , Math121A Sample Final Exam WQ10 4 b) g = GG , = { GG : = } . 7) Let : g be a linear transformation. a) Show that the null space of is a subspace of g . b) Show that the range of is a subspace of . Math121A Sample Final Exam WQ10 5 8) Let g: G () G () be the transformation g() = () () . Let = {2 + , 2 , 1 + } be a basis for G () . Find g . 9) Let g: be a linear transformation with the property that gg( ) = g( ) for every vector . a) Let be the range of g . In other words, = {g( )u } . If , then what is g( ) ? b) If , then what is g( g( )) ?...
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This note was uploaded on 04/22/2010 for the course MATH 3a taught by Professor Staff during the Spring '08 term at UC Irvine.

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SampleFinal - , based on the basis found. a) = , = + + : ,...

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