Test#1-Fall2008_Solution

Test#1-Fall2008_Solution - RIT-Dubai EE 0304-870-32:...

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Unformatted text preview: RIT-Dubai EE 0304-870-32: Mathematics for Engrs I Midterm Examination 1 Name: ___ Solution _________________________ INSTRUCTIONS : 1.Please box your final answers. 2. Do not un-staple the exam under any circumstances. 3. Absolutely no communication between students is allowed during the examination. 4.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: /20 Prob 2: /20 Prob 3: /20 Prob 4: /20 Prob 5: /20 =============== _____________________________________________________________________________ _ EE 0304-807-32 - Prof. S. Dianat Dept. of Electrical Engineering Fall 2008 Midterm Examination 1 Name:_________________________________ Fall 2008 Total: /100 Problem 1: (Each answer is worth 1 point unless indicated otherwise) (20 points) a) Let - = 1 3 9 1 4 12 1 A => Det(3A) = 27 1 27 ) det( 3 3 = = A Det (A 12 ) = 1 )) (det( 12 = A Det (A-1 ) = 1 ) det( 1 = A Det (A T ) = 1 ) (det( = A Trace (A) = 6 1 1 4 = + + Trace (3A+I) 21 3 18 ) ( ) ( 3 = + = + = I Trace A Trace b) = 4 2 1 B => =- 25 . 5 . 1 1 B and Det (2B-1 ) = 1 8 1 8 ) det( 8 1 = = - B c) Let = 1 5 1 c b a A and ---- = 1 1 2 c b a B => Det (BA) = 10 ) 5 )( 2 ( ) det( ) (det(- =- = A B Det (AB 2 ) = 20 ) 4 )( 5 ( )) )(det( (det( 2 = = B A Det (A-1 B-1 ) = 1 . 5 1 2 1 ) det( ) (det( 1 1- = - =-- A B Trace (A+2B) = 11 4 7 ) ( TRace 2 ) ( Trace = + = + B A d ) Let A be factored into a product shown below : - = 2 2 4 3 2 1 1 1 1 1 a d A . Compute the value of Det (A). Answer: Det (A) = 16 16 1 = __________________________________________________________________________ ____ EE 0304-807-32 - Prof. S. Dianat Dept. of Electrical Engineering Fall 2008 Midterm Examination 1 2 Name:_________________________________ Fall 2008 Find 23 a . Answer: 23 a = -3+2=-1 e) Let x 1 = (2, 1, 2) T , x 2 = (6, 3, 6) T and x 3 = (4, 2, -4) T . Are they linearly independent? (2 pts). Please circle: YES f) Let x 1 = (1-j, 1+j, 2) T , and x 2 = (3+j, 2-j, j) T . Compute 8284 . 4 2 2 2 1 1 = + + = x 8284 . 2 2 2 8 4 2 2 2 1 = = = + + = x 2 1 = x 5758 . 11 134 3 2 1 2 = =- x x 3 3 , 2 1 j x x + = < __________________________________________________________________________ ____ EE 0304-807-32 - Prof. S. Dianat Dept. of Electrical Engineering Fall 2008 Midterm Examination 1 3 NO Name:_________________________________ Fall 2008 Problem 2: (Show all work to receive credit) (20 points) Given the following system of equations in Ax = b form: =...
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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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Test#1-Fall2008_Solution - RIT-Dubai EE 0304-870-32:...

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