2010-03-10 - MAT 1332: CALCULUS FOR LIFE SCIENCES JING LI...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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?...
View Full Document

This note was uploaded on 03/19/2011 for the course MAT 1332 taught by Professor Munteanu during the Spring '07 term at University of Ottawa.

Page1 / 7

2010-03-10 - MAT 1332: CALCULUS FOR LIFE SCIENCES JING LI...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online