worksheet11 - Review and Examples (Spr. 2006) Due Thursday...

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Unformatted text preview: Review and Examples (Spr. 2006) Due Thursday 6th April These are examples of questions with the degree of difficulty that you will encounter in the lab-exam. Make sure that you can do them! Use Mathematica to solve all parts of the problems Vectors Problem 1. Show that for any vectors ~a , ~ b , ~ c that, (i) ~a. ( ~a ~ b ) = 0 (ii) ~a. ( ~ b ~ c ) = ( ~a ~ b ) .~ c Lists and Matrices Problem 2. Display the following matrix in matrixform. matrix = {{ . 2 ,- . 4 , . 1 } , { . 4 , . 2 ,- . 3 } , { . 6 ,- . 3 ,- . 1 }} We havent found the eigenvalues and vectors of symmetric matrices be- fore; however, this illustrates the power of mathematica. Look up Eigenvalue in the help manual. You wont fully appreciate the power of this until you have to solve eigenvalue problems by hand in advanced mechanics and quan- tum mechanics. Find the determinant, eigenvalues and eigenvectors of the matrix matrix ....
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This note was uploaded on 07/25/2008 for the course PHY 102 taught by Professor Duxbury during the Spring '08 term at Michigan State University.

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worksheet11 - Review and Examples (Spr. 2006) Due Thursday...

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