2.1 - MATH1850U/2050U: Chapter 2 1 DETERMINANTS In this...

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MATH1850U/2050U: Chapter 2 1 DETERMINANTS In this chapter, we study “determinants”. These will be useful for solving very small linear systems, will provide a formula for the inverse of a matrix, and will help us link various concepts in linear algebra together. Determinants by Cofactor Expansion (Section 2.1; pg. 93) Recall: Back in section 1.4, we had defined the inverse of a 2 2 matrix as: a c b d bc ad A 1 1 provided that 0 bc ad . Definition: If A is a square matrix, then the minor of entry ij a is denoted by ij M and is defined to be the determinant of the submatrix that remains after the i th row and j th column are deleted from A . The number ij j i M ) 1 ( is denoted by ij C and is called the cofactor of entry ij a . Example: Find 11 C and 12 C for the 3x3 matrix 1 2 4 7 8 5 4 3 1 . Theorem:
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This note was uploaded on 10/12/2011 for the course MATH 1020 taught by Professor Paulatu during the Spring '11 term at UOIT.

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2.1 - MATH1850U/2050U: Chapter 2 1 DETERMINANTS In this...

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