nyc.sci._2005-1 - DAWSON COLLEGE MATHEMATICS DEPARTMENT...

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DAWSON COLLEGE MATHEMATICS DEPARTMENT FINAL EXAMINATION LINEAR ALGEBRA 201-NYC-05 (SCIENCE) MAY 2005 9:30-12:30 1. Given the linear system. 12 3 4 34 3 4 20 53 4 2 8 3 15 15 8 xx x x x x −+ − − = += +− = (a) Find the general solution by using Gauss-Jordan elimination. (b) Find the particular solution for which 1 x7 = . 2. Given 25 1 351 3 1 23 xyz xy z −−= −− = +−= (a) Find the inverse of the coefficient matrix. 5 3 21 1 A ⎡⎤ ⎢⎥ =− ⎣⎦ (b) Use the result in (a) to find the solution of the given system of equations. 3. (a) If () 1 2 IA −= find A. (b) Given the matrices. 1 13 ,, 0 1 35 2 31 14 AB C == = , find 1 3 T A BC .
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2 4. (a) Given the matrix abc A def ghi = with ( ) det 2 A = − . find ( ) ( ) ( ) () ( ) ( ) 52 5 2 22 2 333 ga ic hb dg fi eh acb −− ++ + −−− . (b) Use Cramer’s rule to solve for z.
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This note was uploaded on 10/03/2010 for the course PHYS. 203-NYA-05 taught by Professor Ms.simpson during the Fall '09 term at Dawson College.

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nyc.sci._2005-1 - DAWSON COLLEGE MATHEMATICS DEPARTMENT...

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