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chapter3.page08

chapter3.page08 - 8 1 BRIEF INTRODUCTION TO VECTORS AND...

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8 1. BRIEF INTRODUCTION TO VECTORS AND MATRICES So x 1 ( t ) = 4 3 e t - 1 3 e 2 t and x 2 = 8 3 e t + 1 3 e 2 t . They are solution of the following system of differential equations, x 0 1 ( t ) = - x 1 ( t ) + x 2 ( t ) x 0 2 ( t ) = 2 x 1 a 1.3. Eigenvalues and Eigenvectors. If A = a b c d the de- termined of A is defined as | A | = fl fl fl fl a b c d fl fl fl fl = ad - bc. For a 3 × 3 matrix a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 we can compute the matrix as fl fl fl fl fl fl a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 fl fl fl fl fl fl = a 11 fl fl fl fl a 22 a 23 a 32 a 33 fl fl fl fl - a 12 fl fl fl fl a 21 a 23 a 31 a 33 fl fl fl fl + a 13 fl fl fl fl a 21 a 22 a 31 a 32 fl fl fl fl . In Mathcad , type the vertical bar — to bring up the absolute evaluator | | , put the matrix in the place holder and press = to compute
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