04 2 x 2 Matrices

# 04 2 x 2 Matrices - 2 X 2 MATRICES THE DETERMINANT IDENTITY...

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2 X 2 M ATRICES : T HE D ETERMINANT , I DENTITY M ATRIX , AND THE I NVERSE The identity matrix is defined as the matrix such that AI = IA for all square matrices. Therefore the product of a square matrix A and the identity matrix is commutative . In essence, the identity matrix has no effect (same as multiply by 1). For a matrix of order 2 by 2, the identity matrix is = 1 0 0 1 I . Ex . Multiply. = × - 1 0 0 1 2 4 3 1 = - × 2 4 3 1 1 0 0 1 The determinant is a scalar. If a matrix has a non-zero determinant, it is said to be non- singular . If the determinant is zero, the matrix is said to be singular . Singularity or non- singularity is significant for some applications. The determinant of a 2 by 2 matrix is: bc ad d c b a - = det . Ex . Find the determinant of the following matrices. -

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## This note was uploaded on 07/12/2011 for the course MATH 241 taught by Professor Kim during the Fall '08 term at University of Illinois, Urbana Champaign.

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04 2 x 2 Matrices - 2 X 2 MATRICES THE DETERMINANT IDENTITY...

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