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Unformatted text preview: 8 1. BRIEF INTRODUCTION TO VECTORS AND MATRICES
2t So x1 (t) = 4 et - 1 e 2t and x2 = 8 et + 1 e 3 3 3 3 the following system of differential equations, . They are solution of x1 (t) = -x1 (t) + x2 (t) x2 (t) = 2x1 a b c d 1.3. Eigenvalues and Eigenvectors. If A = termined of A is defined as |A| = matrix a b c d the de- = ad - bc. For a 3 3 a11 a12 a13 a21 a22 a23 a31 a32 a33 we can compute the matrix as a11 a12 a13 a21 a22 a23 a31 a32 a33 = a11 a22 a23 a21 a23 a21 a22 -a12 +a13 . a32 a33 a31 a33 a31 a32 In Mathcad , type the vertical bar -- to bring up the absolute evaluator | |, put the matrix in the place holder and press = to compute the determinant. The following screen shot shows an example, Figure 2. Compute determinant in Mathcad The concepts of eigenvalue and eigenvector play an important role in find solutions to system of differential equations. Definition 1.5. We say is an eigenvalue of a matrix A (2 2 or 3 3) if the determinant |A - I| = 0. An nonzero vector v is an eigenvector associated with if Av = v. Remark 1.1. ...
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This note was uploaded on 10/04/2011 for the course MAP 4231 taught by Professor Dr.han during the Spring '11 term at UNF.
- Spring '11