Purdue Linear Algebra Final

Purdue Linear Algebra Final - MATH 265 FINAL EXAM Name and...

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MATH 265 FINAL EXAM Name and ID: Instructor: Section or class time: Instructions: Calculators are not allowed. There are 8 problems in the first part worth 13 points each. There are 12 problems in the second part worth 8 points each. The total is 200 points. 1 2 3 4 5 6 7 8 9 x 10 x 11 x 12 x 1
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Part I You must show all work for problems in first part. 1. Let A = ± 0 a b c ² (a) Find conditions on a, b and c such that A is symmetric. (b) Find conditions on a, b and c such that A has an inverse. (c) Find conditions on a, b and c such that A satisfies A 2 = 0. 2
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2. Consider a linear system whose augmented matrix is of the form 0 t - 7 0 6 0 2 2 t - 2 - 2 1 - 1 - 2 1 (a) For what values of t will the system have no solutions? (b) For what values of t will the system have infinitely many solutions? 3
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3. Find a basis for the subspace of R 4 spanned by v 1 = 0 2 3 0 , v 2 = 1 2 0 1 , v 3 = 1 0 - 3 1 , v 4 = 1 1 0 0 . 4
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4. Let W be the span of (1 , 0 , 2) and (0 , 1 , 0) in R 3 (which is given the standard inner product.) (a) Find a basis for W .
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This note was uploaded on 02/20/2011 for the course MATH 302 taught by Professor Staff during the Fall '08 term at University of Delaware.

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Purdue Linear Algebra Final - MATH 265 FINAL EXAM Name and...

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