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Unformatted text preview: MAT 1332: CALCULUS FOR LIFE SCIENCES JING LI Contents 1. Review: Linear Algebra II – Vectors and matrices 1 1.1. Definition 1 1.2. Operations 1 2. Linear Algebra III – Inverses and Determinants 1 2.1. Inverse Matrices 1 2.2. Determinants 4 2.2.1. Determinants for matrices of size 2 × 2 4 2.2.2. Determinants for matrices of size 3 × 3 5 2.3. Solving system of linear equations using inverse matrices 6 1. Review: Linear Algebra II – Vectors and matrices 1.1. Definition. 1.2. Operations. • Basic matrix opertaions • Matrix-Vector multiplication • Matrix-Matrix multiplication 2. Linear Algebra III – Inverses and Determinants 2.1. Inverse Matrices. Example 1. Definition. Suppose that A = [ a ij ] is an n × n square matrix . If there exists an n × n square matrix B such that AB = BA = I n then B is called the inverse matrix of A and denoted by A- 1 . Note: • If the matrix A has an inverse, A is called invertible or nonsingular . • If A does not have inverse, then A is called singular . • If A is invertible, its inverse matrix is unique ; that is, if B and C are both inverse matrices of A , then B = C . Date : 2010-03-10. 1 2 JING LI • If A an invertible n × n matrix, then ( A- 1 )- 1 = A . • If A and B are invertible n × n matrices, then ( AB )- 1 = B- 1 A- 1 Question 1 for this subsection: How can we find out whether a given matrix has an inverse and what the inverse is?...
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