2010-03-15 - MAT 1332 CALCULUS FOR LIFE SCIENCES JING LI...

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MAT 1332: CALCULUS FOR LIFE SCIENCES JING LI Contents 1. Review: Linear Algebra III – Inverses and Determinants 1 1.1. Inverse Matrices 1 1.2. Determinants 1 1.3. Solving system of linear equations using inverse matrices 1 2. Linear Algebra IV – Eigenvalues and Eigenvectors 1 2.1. Definition 1 2.2. Computation of eigenvalues and eigenvectors 3 1. Review: Linear Algebra III – Inverses and Determinants 1.1. Inverse Matrices. Algorithm to compute an inverse matrix 1.2. Determinants. Determinants for matrices of size 2 × 2 Determinants for matrices of size 3 × 3 1.3. Solving system of linear equations using inverse matrices. 2. Linear Algebra IV – Eigenvalues and Eigenvectors 2.1. Definition. Example 1. Introductory Example: Consider the matix A = 0 1 1 0 so that A x y = y x For example, 1 . A 1 0 = 2 . A 3 - 1 = However, 3 . A 1 1 = Date : 2010-03-15. 1
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2 JING LI 4 . A 1 - 1 = We will be looking at special situations where given a square matrix A and a vector v that product Av will be the same as the scalar multiplication λv
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