ENME361 Quiz 8 Solution

ENME361 Quiz 8 Solution - ENME 361 Fall 2008 Solution for...

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ENME 361 Fall 2008 Solution for Quiz #8 (November 13, 2008; Duration: 10 minutes) 1) Write the following system of governing equations in matrix form: Solution : The matrix form of the governing equations is as follows: 11 1 1 12 2 2 1 22 3 3 2 2 2 () 0 0 x xx f t cc c kk k m c k m x f t +− ⎧⎫ ⎧⎫⎧ ⎡⎤ ++ = ⎨⎬ ⎨⎬⎨ ⎢⎥ −+ ⎣⎦ ⎩⎭ ⎩⎭⎩ ±± ± ± 2) Provide the definition of the following: i) symmetric matrix and ii) identity matrix. Solution : i) A symmetric matrix is a square matrix whose transpose is equal to the matrix itself; that is, [ ] [] T A A = . ii) An identity matrix is a matrix whose diagonal elements are unity and all other entries are
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