Tset%232_Fall_2008_Solution

Tset%232_Fall_2008_Solution - RIT-Dubai EE 0304-870-32:...

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______________________________________________________________________________ EE 0304-807-32 - Prof. S. Dianat Dept. of Electrical Engineering Fall 2008 Midterm Examination II RIT-Dubai EE 0304-870-32: Mathematics for Engrs I Midterm Examination II (Solution) Name: ____________________________ INSTRUCTIONS : 1. Please “box” your final answers. 2. You must show all work (details, derivations, carefully drawn & labeled graphs, equations, etc.) to receive credit. No details = no credit. All derivations must be clearly described showing each mathematical step. Prob 1: /25 Prob 2: /20 Prob 3: /30 Prob 4: /25 =============== Total: /100

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Name:_________________________________ Fall 2008 EE 0304-807-32 - Prof. S. Dianat Dept. of Electrical Engineering Fall 2008 Midterm Examination II 2 Problem 1: (20 points) a) Let 3 4 1 2 1 0 1 0 2 A => 6 3 1 i i 23 3 2 1 8696 . 0 23 20 ) ( 1 A trace b) 3 4 8 0 2 3 0 0 1 B => 1 1 2 2 3 3 c) Let 5 1 3 1 4 2 3 2 1 A 3 2 1 , , x x x are eigenvectors => 0 , 2 1 x x (Matrix is symmetric) 0 , 2 3 x x (Matrix is symmetric) d ) Give an example of a matrix with exactly two zero eigenvalues and no zero entries. 2 4 1 2 A e) Determine whether the following matrices are (1) positive definite (2) positive semidefinite (3) negative definite (4) negative semidefinite
Fall 2008 EE 0304-807-32 - Prof. S. Dianat Dept. of Electrical Engineering Fall 2008 Midterm Examination II 3 1 0 1 0 3 1 1 1 2 A Answer: Positive definite 2 1 1 1 4 1 1 1 1 B Answer: Negative definite 2 1 1 2 C Answer: Positive definite f) For what values of a is the quadratic form xy y ax 2 3 2 2 always positive Answer 3 1 a 0 3 1 1 2 3 2 2 y x a y x xy y ax if 3 1 1 a A is positive definite. Matrix

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This note was uploaded on 11/10/2008 for the course ME 0304.870.3 taught by Professor Sohaildainat during the Fall '08 term at RIT.

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Tset%232_Fall_2008_Solution - RIT-Dubai EE 0304-870-32:...

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